bluuebunny/crossref_metadata_2025 huggingface dataset:
On Stable Diffeomorphism of Exotic Spheres in the Metastable Range
Authors: Antonelli P. L.
Published: December 2010

Let ⊖np+ 1denote the subgroup of the Kervaire-Milnor groupθnconsisting of thosen-spheres which imbed with trivial normal bundle in Euclidean(n + p+ 1)-space,n<2p.It is known that such imbeddings always exist [6], and that the normal bundle is independent of the imbedding[10].Following [2], we write Ωn,pfor the quotientθn/⊖np+ 1.

The order of Ωn,pafter identifying each element with its inverse, is equal to the number of diffeomorphically distinct (orientation preserved) Σn×Sp[2; 5]. Indeed,Ωn,pis closely linked to the problem of determining the number of smooth structuresα(n, p)onSn×Sp.For instance, ifΩn,p= 0 thenα(n, p)equals the order ofθn+p[5]. Specific results are easily read off Table I and Theorem 2.1.
A Sufficient Condition that an Operator Algebra be Self-Adjoint
Authors: Radjavi Heydar , Rosenthal Peter
Published: December 2010

It is well-known, and easily verified, that each of the following assertions implies the preceding ones.

(i)

Every operator has a non-trivial invariant subspace.

(ii)

Every commutative operator algebra has a non-trivial invariant subspace,

(iii)

Every operator other than a multiple of the identity has a non-trivial hyperinvariant subspace.

(iv)

The only transitive operator algebra on is

Note. Operator means bounded linear operator on a complex Hilbert space , operator algebra means weakly closed algebra of operators containing the identity, subspace means closed linear manifold, a non-trivial subspace is a subspace other than {0} and , a. hyperinvariant subspace for A is a subspace invariant under every operator which commutes with A, a transitive operator algebra is one without any non-trivial invariant subspaces and denotes the algebra of all operators on .
Representations of Groups as Automorphisms on Orthomodular Lattices and Posets
Authors: Gudder Stanley P.
Published: December 2010

In this paper we study the problem of representing groups as groups of automorphisms on an orthomodular lattice or poset. This problem not only has intrinsic mathematical interest but, as we shall see, also has applications to other fields of mathematics and also physics. For example, in the “quantum logic” approach to an axiomatic quantum mechanics, important parts of the theory can not be developed any further until a fairly complete study of the representations of physical symmetry groups on orthomodular lattices is accomplished [1].

We will consider two main topics in this paper. The first is the analogue of Schur's lemma and its corollaries in this general setting and the second is a study of induced representations and systems of imprimitivity.
Multiplicative Integration of Infinite Products
Authors: Lovelady David Lowell
Published: December 2010

Let G be a complete normed abelian group with norm N1. Let S be an interval (bounded or otherwise) of real numbers. We propose to study the Stieltjes integral equation

where p is in G, a is in S, and each Fk is a function on S each value of which is a function from G to G. Our primary tools of investigation will be the works of J. S. MacNerney [6; 7] and their extensions by the author [4; 5]. Our main result, Theorem 4, will show that the equation above can be solved by a product integral of infinite products of solutions for the summands of the integrator. After obtaining our results, we shall specialize them to a linear situation and then show how this specialization allows us to obtain representations for analytic functions having only invertible values in a complex Banach algebra with identity.
Sphere Packings and Error-Correcting Codes
Authors: Leech John , Sloane N. J. A.
Published: December 2010

Error-correcting codes are used in several constructions for packings of equal spheres in n-dimensional Euclidean spaces En. These include a systematic derivation of many of the best sphere packings known, and construction of new packings in dimensions 9-15, 36, 40, 48, 60, and 2m for m ≧ 6. Most of the new packings are nonlattice packings. These new packings increase the previously greatest known numbers of spheres which one sphere may touch, and, except in dimensions 9, 12, 14, 15, they include denser packings than any previously known. The density Δ of the packings in En for n = 2m satisfies

In this paper we make systematic use of error-correcting codes to obtain sphere packings in En, including several of the densest packings known and several new packings.
The Minimal Prime Spectrum of a Commutative Ring
Authors: Hochster M.
Published: December 2010

We call a topological space X minspectral if it is homeomorphic to the space of minimal prime ideals of a commutative ring A in the usual (hull-kernel or Zariski) topology (see [2, p. 111]). Note that if A has an identity, is a subspace of Spec A (as defined in [1, p. 124]). It is well known that a minspectral space is Hausdorff and has a clopen basis (and hence is completely regular). We give here a topological characterization of the minspectral spaces, and we show that all minspectral spaces can actually be obtained from rings with identity and that open (but not closed) subspaces of minspectral spaces are minspectral (Theorem 1, Proposition 5).
Connectivity of Function Spaces
Authors: Borges Carlos R.
Published: December 2010

Given two spaces X and Y with Y either an AE (metrizable) or ANE (metrizable), little is known with regard to when the function space (Yx, τ), for some topology τ, is an AE (metrizable) or ANE (metrizable) except when very strong separation properties are imposed on X and Y (see [5, pp. 186-189]). One of our tasks will be to eliminate most of these separation property requirements, therefore complementing or extending some of the results of [5]. We also attach an appendix, which contains some needful information, as well as the complete local analogue of [2, Theorem 5.1].

Throughout, we use either the terminology and notation of [2] or of the appendix. We also let co stand for the compact-open topology and pc stand for the pointwise convergence topology of any function space
Invariant Means on Dense Subsemigroups of Topological Groups
Authors: To-Ming Lau Anthony
Published: December 2010

Let S be a topological semigroup (i.e., S is a semigroup with a Hausdorff topology such that the mapping from S × S to S defined by (s, t) → s ⋅ t for all s, t in S is continuous when S × S has the product topology) and C(S) be the space of bounded continuous real valued functions on S. For each ƒ in C(S) and a in S, define || ƒ || = sup {|ƒ(s)|: s ∈ S} (sup norm of ƒ); raƒ(s) = ƒ(sa) and laƒ(s) = ƒ(as) for all s in S.
Varieties of Orthomodular Lattices
Authors: Bruns Günter , Kalmbach Gudrun
Published: December 2010

In this paper we start investigating the lattice of varieties of orthomodular lattices. The varieties studied here are those generated by orthomodular lattices which are the horizontal sum of Boolean algebras. It turns out that these form a principal ideal in the lattice of all varieties of orthomodular lattices. We give a complete description of this ideal; in particular, we show that each variety in it is generated by its finite members. We furthermore show that each of these varieties is finitely based by exhibiting a (rather complicated) finite equational basis for each variety.

Our methods rely heavily on B. Jonsson's fundamental results in [8]. This, however, could be avoided by starting out with the equations given in sections 3 and 4. Some of our arguments were suggested by Baker [1],
Quasi-Injectivité de Certains Modules sur Leur Anneau D'endomorphismes
Authors: Cailleau Annie
Published: December 2010

Dans tout ce qui suit, R désigne un anneau unitaire. Soit M R un R-module à droite; M R est muni canoniquement d'une structure de module à gauche sur l'anneau Λ de ses endomorphismes, pour laquelle il sera noté AM.

On sait [3, Théorème 3.1] que si M R est quasi-injectif à sous-module singulier nul, Λ est un anneau régulier au sens de Von Neumann, auto-injectif à droite. Dans [5] B. Osofsky étudie l'auto-injectivité à gauche de Λ et pose les problèmes suivants.

(1) Si MR est un module injectif à sous-module singulier nul, et si Λ est auto-injectif à gauche, ΛM est-il injectif?

(2) Si Ton remplace l'hypothèse M R injectif par M R quasi-injectif, ΛM est-il quasi-injectif?

On apporte ici une réponse affirmative à ces deux questions lorsque R est un anneau commutatif (Théorèmes 7 et 8).
A Characterization of Spin Representations
Authors: Brown Robert B.
Published: December 2010

Associated with a non-degenerate symmetric bilinear form on a vector space is a Clifford algebra and various Clifford groups, which have spin representations on minimal right ideals of the Clifford algebra. Several invariants for these representations have been known for some time. In this paper the forms are assumed to be “split”, and several relations between the invariants are derived and promoted to the status of axioms. Then it is shown that any system satisfying the axioms comes from a minimal right ideal in a Clifford algebra and that the automorphism groups associated with the system are the Clifford groups. Hence, the axioms characterize spin representations.

A description of split forms and spin representations is in section two. In section three the invariants and their properties are described.
The Free Product of Two Groups with a Malnormal Amalgamated Subgroup
Authors: Karrass A. , Solitar D.
Published: December 2010

In [1], B. Baumslag defined a subgroup U of a group G to be malnormal in G if gug–1 ∈ U, 1 ≠ u ∈ U, implies that g ∈ U. Baumslag considered the class of amalgamated products (A * B; U) in which U is malnormal in both A and B. These amalgamated products play an important role in the investigations of B. B. Newman [13] of groups with one defining relation having torsion. In this paper, we shall be concerned primarily with a generalization of this class.

Let U be a subgroup of a group G and let u ∈ U. Then the extended normalizer EG(u, U) of u relative to U in G is defined by

if u ≠ 1, and by EG(u, U) = U if u = 1.
Fundamental Biorthogonal Sequences and K-Norms on ϕ
Authors: Crone L. , Fleming D. J. , Jessup P.
Published: December 2010

A biorthogonal sequence is a double sequence (xi,fi) where each xi is from some locally convex space X, each fi is from X* and fi(xj) = δij. A biorthogonal sequence is called total if the functionals (fi) are total over X and is called fundamental if sp(xi) is dense in X. If a biorthogonal sequence is both total and fundamental we refer to it as a Markushivich basis or, more simply, an M-basis.

If (xi,fi) is a total biorthogonal sequence for X, then X can be identified with the space of all scalar sequences (fi(x)) under the correspondence x ↔ (fi(x)). We refer to this space as the associated sequence space with respect to (xi, fi). With this correspondence, xi corresponds to and fi corresponds to Ei, the ith coordinate functional.
Normed Linear Spaces that are Uniformly Convex in Every Direction
Authors: Day M. M. , James R. C. , Swaminathan S.
Published: December 2010

The concept of uniform convexity in a normed linear space is based on the geometric condition that if two members of the unit ball are far apart, then their midpoint is well inside the unit ball. We consider here a generalization of this concept whose geometric significance is that the collection of all chords of the unit ball that are parallel to a fixed direction and whose lengths are bounded below by a positive number has the property that the midpoints of the chords lie uniformly deep inside the unit ball. This notion, called uniform convexity in every direction (UCED), was first used by A. L. Garkavi [5; 6] to characterize normed linear spaces for which every bounded subset has at most one Čebyŝev center. We discuss questions of renorming spaces so as to be UCED and forming products of spaces that are uniformly convex in every direction.
Special (p;q) Radicals
Authors: McKnight J. D. , Musser Gary L.
Published: December 2010

In [3], the study of (p;q) radicals was initiated. In this paper, the integral polynomials p(x) and q(x) which determine the Jacobson radical are characterized and the Jacobson radical is shown to be the only semiprime (p;q) radical for which all fields are semisimple. Also, it is observed that the prime, nil, and Brown-McCoy radicals are not (p;q) radicals. To show that the semiprime (p;q) radicals are special and that they can be determined by subclasses of the class of primitive rings, a classification theorem for (p;q)-regular primitive rings is given. Finally, it is shown that the collection of semiprime (p;q) radicals and the collection of semiprime (p;1) radicals coincide.
A Functional Analytic Description of Normal Spaces
Authors: Binz E. , Feldman W.
Published: December 2010

Throughout the paper, X will denote a completely regular (Hausdorff) topological space and C(X) the R-algebra of all real-valued continuous functions on X. When this algebra carries the continuous convergence structure [1], we write CC(X). We note that CC(X)is a complete [5] convergence R-algebra [1].

Our description of normality reads as follows. A completely regular topological space X is normal if and only if CC(X)/J (endowed with the obvious quotient structure; see § 1) is complete for every closed ideal J ⊂ CC(X).
Indecomposable Vector Bundles on the Projective Line
Authors: Roberts Leslie G.
Published: December 2010

Let A be a commutative ring, and let Proj A[t0, ti]. By a vector bundle on X we mean a locally free sheaf of finite rank on X. Set t = t1/to. Then X is made up of two affine pieces U1 = Spec A[t], and U2 = Spec A[t-1]. Let P(R) denote the category of finitely generated projective modules over the ring R. The category of vector bundles on X is equivalent to the category of triples (P1,f1, P2), where P1 ∊ 𝓅 (A[t]), P2 ∊ 𝓅(A[t-1]), and

is an A[t, t-1] -isomorphism. In [2], the category of vector bundles on is denned directly in this manner, without first defining (so that one could work over a non-commutative ring). We prove that if A is a Krull ring (or a Noetherian ring with connected spec) of dimension > 0, then there is an indecomposable vector bundle of rank n on X, for every positive integer n.
Sums and Products of Normal Functions
Authors: Bash David W.
Published: December 2010

Let D be the unit disk in the complex plane. Let p(z, z’) denote the hyperbolic distance between z and z’ in ((1 + u)/ (1 — u)) = tanh-1 u, [6, chapter 15]). Let W be the Riemann sphere with the chordal metric. A complex valued function F(Z) in D is a normal function if lor each pair of sequences {zn} and {zn’} of points in D such that the convergence of {(fzn)} to a value α in W implies the convergence of {f(zn’)} to α. Two sequences {zn} and {zn’} of points in D are called close sequences if ρ(zn, zn’) → 0. (There are several equivalent definitions of normality if the functions are meromorphic.) The definition of a normal function implies that a normal function is continuous at each point of D when using the Euclidean metric in the domain and the chordal metric in the range.

We wish to study the sums and products of normal functions. Some functions, such as a function in a Hardy p-class, p > 0, (or really any function of bounded characteristic) can be written as a sum or product of two normal functions, but sums and products of normal functions need not be normal (see Lappan [7]).
Local Topological Properties and One Point Extensions
Authors: Mack John , Rayburn Marlon , Woods Grant
Published: December 2010

In 1957, Mrowka [12] showed that a locally paracompact space admits a one point paracompactification (see also [2, Chapter 9, § 4, Exercise 27]). Similarly, in [9] Isiwata obtained a one point realcompactincation for locally realcompact spaces. Recently a number of authors (see [11, 16; 17; 18; 21]) have constructed one point P-extensions of local P-spaces for a variety of topological properties P. It is the purpose of this paper to draw together the various techniques used by the above mentioned authors and to study the set (lattice) of all one point P-extensions of a particular space.
Uniformities on a Product
Authors: Hager Anthony W.
Published: December 2010

All topological spaces shall be uniformizable (completely regular Hausdorff). A uniformity on X shall be viewed as a collection μ of coverings of X, via the manner of Tukey [20] and Isbell [16], and the associated uniform space denoted μX. Given the uniformizable topological space X, we shall be concerned with compatible uniformities as follows (discussed more carefully in § 1). The fine uniformity α (finest compatible with the topology); the “cardinal reflections“ αm of α (m an infinite cardinal number) ; αc, the weak uniformity generated by the real-valued continuous functions.

With μ standing, generically, for one of these uniformities, we consider the question: when is μ(X × Y) = μX × μY For μ = αℵ0 (the finest compatible precompact uniformity), the problem is equivalent to that of when

β(X × Y) = βX × βY,

β denoting Stone-Cech compactification; this is answered by the theorem of Glicksberg [9]. For μ = α, we have Isbell's generalization [16, VI1.32].
A Generalization of “Concordance of PL-Homeomorphisms of Sp × Sq
Authors: Hodgson J. P. E.
Published: December 2010

Let Mm be a closed PL manifold of dimension m. Then a concordance between two PL-homeomorphisms h0, h1:M → M is a PL-homeomorphismH: M × I → M × I such that H|M × 0 = h0 and H|M × 1 = h. Concordance is an equivalence relation and in his paper [2], M. Kato classifies PL-homeomorphisms of Sp × Sq up to concordance. To do this he treats first the problem of classifying those homeomorphisms that induce the identity in homology, and then describes the automorphisms of the cohomology ring that can arise from homeomorphisms of Sp × Sq. In this paper we show that for sufficiently connected PL-manifolds that embed in codimension 1, one can extend Kato's classification of the homeomorphisms that induce the identity in homology.
The Torsion Submodule of A Cyclic Module Splits Off
Authors: Teply Mark L.
Published: December 2010

A prominent question in the study of modules over an integral domain has been: “When is the torsion submodule t(A) of a module A a direct summand of A?” A module is said to split when its torsion module is a direct summand. Clearly, every cyclic module over an integral domain splits. Interesting splitting problems have been explored by Kaplansky [14; 15], Rotman [20], Chase [4], and others.

Recently, many concepts of torsion have been proposed for modules over arbitrary associative rings with identity. Two of the most important of these concepts are Goldie's torsion theory (see [1; 12; 22]) and the simple torsion theory (see [5; 6; 8; 9; 23], and their references).
Projective Homotopy Classes of Stiefel Manifolds
Authors: Strutt Joseph
Published: December 2010

Given a homotopy class [f] in πn(X), we say that [f] is projective if and only if there is a homotopy commutative factorization

where v is the standard double covering. We then denote by the subset of projective homotopy classes in πn(X).

The notion of projective homotopy classes was studied in the author's thesis [5], and the projective homotopy classes for spheres in the stable range, up through the 3-stem were calculated in [6].
C(X) As A Dual Space
Authors: Manes E. G.
Published: December 2010

It is known [1] that for compact Hausdorff X, C(X) is the dual of a Banach space if and only if X is hyperstonian, that is the closure of an open set in X is again open and the carriers of normal measures in C(X)* have dense union in X. With the desiratum of proving that C(X) is always the dual of some sort of space we broaden the concept of Banach space as follows. A Banach space may be comfortably regarded as a pair (E, B) where E is a topological linear space and B is a subset of E ; the requisite property is that the Minkowski functional of B be a complete norm whose topology coincides with that of E.
Intersections of Primary Ideals in Rings of Continuous Functions
Authors: Williams R. Douglas
Published: December 2010

Let C be the ring of all real valued continuous functions on a completely regular topological space. This paper is an investigation of the ideals of C that are intersections of prime or of primary ideals.

C. W. Kohls has analyzed the prime ideals of C in [3 ; 4] and the primary ideals of C in [5]. He showed that these ideals are absolutely convex. (An ideal I of C is called absolutely convex if |f| ≦ |g| and g ∈ I imply that f ∈ I.) It follows that any intersection of prime or of primary ideals is absolutely convex. We consider here the problem of finding a necessary and sufficient condition for an absolutely convex ideal I of C to be an intersection of prime ideals and the problem of finding a necessary and sufficient condition for I to be an intersection of primary ideals.
Riemann Surfaces as Orbit Spaces of Fuchsian
Groups
Authors: Moore M. J.
Published: December 2010

A Fuchsian group is a discrete subgroup of the hyperbolic
group, L.F. (2, R), of linear fractional
transformations

each such transformation mapping the complex upper half plane
D into itself. If Γ is a Fuchsian group, the orbit space
D/Γ has an analytic structure such that the projection
map p: D → D/Γ, given by
p(z) = Γz, is holomorphic
and D/Γ is then a Riemann surface.

If N is a normal subgroup of a Fuchsian group Γ, then
N is a Fuchsian group and S = D/N is a
Riemann surface. The factor group, G =
Γ/N, acts as a group of automorphisms (biholomorphic
self-transformations) of S for, if γ ∊ Γ and z ∊
D, then γN ∊ G, Nz ∊ S, and
(γN) (Nz) =
Nγz. This is easily seen to be independent of
the choice of γ in its N-coset and the
choice of z in its N-orbit.

Conversely, if S is a compact Riemann surface, of genus at
least two, then S can be identified with
D/K, where K is a Fuchsian group acting
without fixed points in D.
A Characterization of the Tits' Simple Group
Authors: Parrott David
Published: December 2010

In [6], J. Tits has shown that the Ree group 2F4(2) is not simple but possesses a
simple subgroup of index 2.
In this paper we prove the following theorem:

THEOREM. Let G be a finite group of even order and let z be an
involution contained in G. Suppose H = CG(z) has the following
properties:

(i) J = O2(H) has order 29and is of class at least 3.

(ii) H/J is isomorphic to the Frobenius group of order
20.

(iii) If P is a Sylow 5-subgroup of H, then
Cj(P) ⊆ Z(J).

Then G = H • O(G) or G ≊
, the
simple group of Tits, as defined in [6].

For the remainder of the paper, G will denote a finite
group which satisfies the hypotheses of the theorem as well as G ≠
H • O(G). Thus Glauberman's theorem
[1] can be applied to G and we have that
〈z〉 is not weakly closed in H (with
respect to G). The other notation is standard (see
[2], for example).
Rational Tensor Representations of Hom(V, V)
and an Extension of an Inequality of I. Schur.
Authors: Marcus Marvin , Gordon William Robert
Published: December 2010

Let V be an n-dimensional vector space
over the complex numbers equipped with an inner product (x,
y), and let (P, μ) be a symmetry class in the
mth tensor product of V associated with a
permutation group G and a character χ (see
below). Then for each T ∊ Hom (V, V) the
function φ which sends each m-tuple
(v1, … , vm) of elements of
V to the tensor μ(TV1, … ,
Tvm) is symmetric with respect to
G and x, and so there is a unique linear map
K(T) from P to P such that φ =
K(T)μ.

It is easily checked that K: Hom(V, V) →
Hom(P, P) is a rational representation of the
multiplicative semi-group in Hom(V, V): for any two linear
operators S and T on V

K(ST) = K(S)K(T).

Moreover, if T is normal then, with respect to the inner
product induced on P by the inner product on V (see below),
K(T) is normal.
On Scalar Dependent Algebras
Authors: Coughlin Raymond , Rich Michael
Published: December 2010

The intent of this paper is to study a class of algebras which do not
necessarily obey the association law but instead obey a law which bears a
marked resemblance to associativity. For lack of a better name we call this
class the class of scalar dependent algebras. Specifically, an algebra
A over a field F is called
scalar dependent if there is a map g: A
× A × A → F such that (xy)z = g(x,
y, z)x(yz), for all
x, y, z in A. To obtain our results we
shall assume throughout that A is a scalar dependent
algebra with an identity element e over a field of
characteristic not 2 satisfying

(I) (x, x, x) = 0.

As usual, the associator (x,y,z) is defined by
(x,y,z) = (xy)z —
x(yz). An example is given to show that
(I) is not implied by scalar dependency.
On the β-Construction in
K-Theory
Authors: Naylor C. M.
Published: December 2010

The β-construction assigns to each complex representation
φ of the compact Lie group G a unique
element β(φ) in (G). For the details of this
construction the reader is referred to [1] or [5].
The purpose of the present paper is to determine some of the properties of
the element β(φ) in terms of the invariants of the
representation φ. More precisely, we consider the following
question. Let G be a simple, simply-connected compact Lie group and let
f : S3 →G be a Lie group homomorphism. Then (S3) ⋍ Z with generator
x = β(φ1), φ1 the fundamental representation of S3 , so that if
φ is a representation of
G,f*(φ) = n(φ)x, where
n(φ) is an integer depending on φ and
f . The problem is to determine n(φ).

Since G is simple and simply-connected we may assume that
ch2, the component of the Chern character in dimension 4 takes
its values in H4(SG,Z)≅Z. Let u be a generator of
H4(SG,Z) so that ch2(β (φ)) = m(φ)u, m(φ)
an integer depending on φ.
Rearrangement Inequalities
Authors: Day Peter W.
Published: December 2010

In recent years a number of inequalities have appeared which involve
rearrangements of vectors in Rn and of measurable functions on a finite measure space. These
inequalities are not only interesting in themselves, but also are important
in investigations involving rearrangement invariant Banach function spaces
and interpolation theorems for these spaces [2; 8; 9].
Unique Factorization Theorems for Subalgebras of the Incidence
Algebra
Authors: Yocom K. L.
Published: December 2010

H. Scheid [4] has found necessary and sufficient conditions on a partially
ordered set S(≦) which is a direct sum of
a countable number of trees for a certain subalgebra G(+, *) of the
incidence algebra F(+, *) to be an
integral domain. In this paper we prove that under similar conditions on
S, G(+, *) is actually a unique factorization domain or,
failing this, that there is a subalgebra
H(+, *) of
F(+, *) which is a unique factorization
domain and contains G. Similar results are then obtained as
corollaries in the regular convolution rings of Narkiewicz.
Right Quotient Rings of a Right LCM Domain
Authors: Beauregard Raymond A.
Published: December 2010

In this paper we continue our investigation of the class of right LCM
domains which was introduced in [2]. A right LCM domain is an
(not necessarily commutative) integral domain with unity in which the
intersection of any two principal right ideals is again principal. In this
note we study the right quotient rings of such a ring. In Section 1 we
describe some of the characteristic properties of right quotient monoids
with respect to which quotient rings are formed. Three particular types of
quotient rings are described in Section 2. In Section 3 we relate the right
ideals of a ring to those of its quotient ring.
Moore Spaces, Semi-Metric Spaces and Continuous Mappings Connected with Them
Authors: Pareek C. M.
Published: December 2010

In [1] Arhangel'skiĭ announced that any σ-paracompact p-space could be mapped onto a Moore space by a perfect map. However Burke [3] recently showed that this is not true in general and he gave an example of a T2, locally compact, σ-paracompact space which cannot be mapped onto a Moore space by a perfect map.
Multiplications on a Space with Finitely Many Non-Vanishing Homotopy Groups
Authors: Cheng Chao-Kun
Published: December 2010

Copeland [1] proved that if X is a CW complex then the set of homotopy classes of multiplications is in 1-1 correspondence with the loop [X ∧ X, X], But in general [X ∧ X, X] is very hard to compute.

Here we study the problem of finding how many different (up to homotopy) multiplications can be put on a space with finitely many non-vanishing homotopy groups. We reduce this problem to computing quotients of certain cohomology groups and to determining the primitive elements (Theorem 3.6). Our approach to this problem uses Postnikov decompositions and multiplier arguments.
An Application of Ultraproducts to Lattice-Ordered Groups
Authors: Glass A. M. W.
Published: December 2010

Using ultraproducts, N. R. Reilly proved that if G is a representable lattice-ordered group and J is an independent subset totally ordered by ≺, then the order on G can be extended to a total order which induces ≺ on J (see [5]). In [4], H. A. Hollister proved that a group G admits a total order if and only if it admits a representable order and, moreover, every latticeorder on a group is the intersection of right total orders. The purpose of this paper is to provide a partial converse, viz: if G is a lattice-ordered group and J is an independent subset totally ordered by ≺, then the order on G can be extended to a right total order which induces ≺ on J.
On a Theorem of Cohen and Lyndon About Free Bases for Normal Subgroups
Authors: Karrass A. , Solitar D.
Published: December 2010

Let S(≠1) be a subgroup of a group G. We consider the question: when are the conjugates of S “as independent as possible“? Specifically, suppose SG (the normal subgroup generated by S in G) is the free product II*S0α where and gα ranges over a subset J of G. Then J must be part of a (left) coset representative system for G mod SG. N where N is the normalizer of S in G. (For, g ∊ SGgαN implies Sg is conjugate to Sgα in SG; however, distinct non-trivial free factors of a free product are never conjugate.)

We say that SG is the free product of maximally many conjugates of S in G if SG = II*Sgα where gα ranges over a (complete) left coset representative system for G mod SGN (or equivalently, gα ranges over a double coset representative system for G mod (SG, N)); in this case we say briefly that S has the fpmmc property in G.
Degrees in Which the Recursive Sets are Uniformly Recursive
Authors: Jockusch Carl G.
Published: December 2010

One of the most fundamental and characteristic features of recursion theory is the fact that the recursive sets are not uniformly recursive. In this paper we consider the degrees a such that the recursive sets are uniformly of degree ≦a and characterize them by the condition a’ ≦ 0". A number of related results will be proved, and one of these will be combined with a theorem of Yates to show that there is no r.e. degree a < 0’ such that the r.e. sets of degree ≦a are uniformly of degree ≦a. This result and a generalization will be used to study the relationship between Turing and many-one reducibility on the r.e. sets.
Presentations of the Groups SL(2,m) And PSL(2,m)
Authors: Sunday J. G.
Published: December 2010

In this paper, we refine the presentations of Behr and Mennicke [1] for SL(2,m)and PSL(2,m)wheremis odd. The group SL(2,m)is first shown to be presented by the following system of generators and relations:

1.1

The group PSL(2,m)appears as the factor group

1.2

This simplification then permits us to use the results of Schur [3] to establish three-relation presentations for these groups.
High Order Derivations and High Order Lie-Like Elements
Authors: Chang S. T.
Published: December 2010

We can define high order derivations of an algebra into the ground field by diagrams. Then consider the same diagrams in t he category of coalgebras. By reversing all t he arrows in these diagrams, we come to a new notion - high order Lie-like elements of a coalgebra. These elements are useful in the study of the structure of coalgebras and sequences of divided powers.
A General Hewitt-Yosida Decomposition
Authors: Traynor Tim
Published: December 2010

In 1952, E. Hewitt and K. Yosida [3] proved that a bounded, finitely additive real-valued set function has a unique representation as the sum of a countably additive function and a “purely finitely additive” function.

Below, using a variation of the Carathéodory process we give a suitable generalization to s-bounded vector-valued set functions. In fact, since the methods do not rely on scalar multiplication, we give the result for commutative Hausdorff topological groups.
Product Maps and Countable Paracompactness
Authors: Martin Harold W.
Published: December 2010

In all that follows, we let S denote the space {0, 1, 1/2, … , 1/n, …} with the relative usual topology and i : S → S denote the identity map on S. In this note, by a map or mapping we always mean a continuous surjection. A map f : X → Y is said to be hereditarily quotient if y ∊ int f(V) whenever V is open in X and f-1(y) ⊂ V. E. Michael has defined a map f : X → Y to be bi-quotient if whenever is a collection of open sets in X which covers f-1(y), there exists finitely many f(V), with V ∊ , which cover some neighbourhood of y.
A Theorem for Enumerating Certain Types of Collections
Authors: Osterweil Leon
Published: December 2010

In this paper, we are concerned with proving a formula for the computation of what is variously called the pattern inventory (e.g., see De Bruijn [2]) or the configuration counting series (e.g., see Harary [3]). Rather than redeveloping a large number of definitions, we shall assume the reader is already familiar with the terminology used by De Bruijn [2].

Polya, in a celebrated paper [4], proved a formula for computing the pattern inventory for all functions f defined on a set D (where D is acted on by a permutation group G), and mapping into a set R (which is called the store) for which the “store enumerator” in known.
Isometries of Hp(Un)
Authors: Schneider R. B.
Published: December 2010

Forelli in [1] has described the isometries of Hp(U) into Hp(U) for p≠2, 0 < p < ∞. We shall extend his methods to characterize the isometries of Hp(Un) onto Hp(Un).

The notation we shall use can be found in Rudin [3].

Let II represent a permutation that induces a map on functions of n complex variables by

Clearly II is an isometry of Hp(Un) onto Hp(Un).
The Classification of Factors is not Smooth
Authors: Woods E. J.
Published: December 2010

There is a natural Borel structure on the set F of all factors on a separable Hilbert space [3]. Let denote the algebraic isomorphism classes in F together with the quotient Borel structure. Now that various non-denumerable families of mutually non-isomorphic factors are known to exist [1; 6; 8; 10; 11; 12; 13], the most obvious question to be resolved is whether or not is smooth (i.e. is there a countable family of Borel sets which separate points). We answer this question negatively by an explicit construction.
Plücker Coordinates for Regular Chain Groups
Authors: Kambayashi T.
Published: December 2010

The theory of Plücker coordinates and Grassmann varieties is well-developed and well-known among the algebraic geometers. It gives a one-to-one correspondence between the set of all subspaces of a given dimension in the ambient projective space and the set of points on a certain projective algebraic variety called a Grassmann variety. The unacquainted can find the theory discussed in detail in Hodge-Pedoe [1, Chapters VII and XIV].
The Algebra of Differentials of Infinite Rank
Authors: Brown W. C.
Published: December 2010

Let k and A denote commutative rings with identity and assume that A is a k-algebra. A qth order k-derivation δ of A into an A -module V is an element of Homk(A, V) such that for any q + 1 elements a0, … , aq of A, the following identity holds:

Thus, a 1st-order derivation is just an ordinary derivation of A into V.
Generalized Spectral Theory and Second Order Ordinary Differential Operators
Authors: Sussmann Héctor J.
Published: December 2010

This paper continues the study, begun in [7], of the spectral theory of non-self-ad joint second order ordinary differential operators on a half-line. The case of a ‘Very small” potential was studied in [4; 5; 6]. The case considered in [7], and in the present paper, is that where the potential is not so small.
Integral Limit Laws for Additive Functions
Authors: Galambos J.
Published: December 2010

In the present paper a general form of integral limit laws for additive functions is obtained. Our limit law contains Kubilius’ results [5] on his class H. In the proof we make use of characteristic functions (Fourier transforms), which reduces our problem to finding asymptotic formulas for sums of multiplicative functions. This requires an extension of previous results in order to enable us to take into consideration the parameter of the characteristic function in question. We call this extension a parametric mean value theorem for multiplicative functions and its proof is analytic on the line of [4].
From Path Lifting and Unique Arc Lifting to Unique Path Lifting
Authors: Bell Harold , Ungar Gerald S.
Published: December 2010

In [4] it was conjectured that a light map p : E → B for which paths can be lifted and lifting of arcs is unique is a Serre fibration. As is well-known this implies that paths have unique liftings. In this paper we shall prove several special cases of this conjecture.

The two main theorems are: (3.5) Let p be a light compact map of a metric space E onto a connected semi-locally contractible along arcs metric space B. If arcs can be lifted uniquely then p is locally trivial.
Non-Existence Criteria for Small Configurations
Authors: Longyear Judith Q.
Published: December 2010

For graph theoretic terms, see Tutte [1], A rank 2 tactical configuration of girth2gand order(s, t)may be regarded as a (1 +s,1 +t)-regularbipartite graph of girth2g.We assumes ≦ t.Using a technique of Friedman [2] we show (i) and (ii).
Compactness and Strong Separation
Authors: Cook David E.
Published: December 2010

Two point sets H and K are said to be strongly separated if there exist two mutually exclusive domains DH and DK containing H and K respectively such that either and are mutually exclusive or · is R. L. Moore has shown [2, Theorem 153, Chapter I] that if S is a normal Moore space and H and K are two mutually separated point sets then H and K are strongly separated. In this paper it is shown that if 5 is a Moore space, (1) H and K are two mutually separated point sets and (2) the closure of the set of all boundary points of H which do not belong to is compact, then H and K are strongly separated.
Groups and Monoids of Regular Graphs (And of Graphs with Bounded Degrees)
Authors: Hell Pavol , Nešetřil Jaroslav
Published: December 2010

A graph X is a set V(X) (the vertices of X) with a system E(X) of 2-element subsets of V(X) (the edges of X). Let X, Y be graphs and f : V(X) → V(Y) a mapping; then/ is called a homomorphism of X into F if [f(x),f(y)] ∈ E(Y) whenever [x,y] ∈ E(X). Endomorphisms, isomorphisms and automorphisms are defined in the usual manner.

Much work has been done on the subject of representing groups as groups of automorphisms of graphs (i.e., given a group G, to find a graph X such that the group of automorphisms of X is isomorphic to G). Recently, this was related to category theory, the main question being as to whether every monoid (i.e., semigroup with 1) can be represented as the monoid of endomorphisms of some graph in a given category of graphs.
Equationally Compact Artinian Rings
Authors: Haley David K.
Published: December 2010

By a Noetherian (Artinian) ring=(R;+ , —, 0, ·) we mean an associative ring satisfying the ascending (descending) chain condition on left ideals. An arbitrary ringis said to beequationally compactif every system of ring polynomial equations with constants inis simultaneously solvable inprovided every finite subset is. (The reader is referred to [2; 8; 13; 14] for terminology and relevant results on equational compactness, and to [4] for unreferenced ring-theoretical results.) In this report a characterization of equationally compact Artinian rings is given - roughly speaking, these are the finite direct sums of finite rings and Prüfer groups; as consequences it is shown that an equationally compact ring satisfying both chain conditions is always finite, as is any Artinian ring which is a compact topological ring.
The Osculatory Packing of a Three Dimensional Sphere
Authors: Boyd David W.
Published: December 2010

Packings by unequal spheres in three dimensional space have interested many authors. This is to some extent due to the practical applications of such investigations to engineering and physical problems (see, for example, [16; 17; 31]). There are a few general results known concerning complete packings by spheres in N-dimensional Euclidean space, due mainly to Larman [20; 21]. For osculatory packings, although there is a great deal of specific knowledge about the two-dimensional situation, the results for higher dimensions, such as [4], rely on general methods which do not give particularly precise information.
On the Structure of Q2(G) for Finitely Generated Groups
Authors: Losey Gerald
Published: December 2010

Let G be a group, ZG its integral group ring and Δ = Δ(G) the augmentation ideal of ZG. Denote by Gi the ith term of the lower central series of G. Following Passi [3], we set . It is well-known that (see, for example [1]). In [3] Passi shows that if G is an abelian group then , the second symmetric power of G.
Classes of Semilattices Associated with an Equational Class of Lattices
Authors: Gaskill H. S.
Published: December 2010

In this paper we consider the question of whether there is a natural class of semilattices associated with a fixed equational class of lattices. We give four classes of semilattices which may be obtained from a given equational class of lattices and show that for the distributive case they coalesce into one class. An incomplete set of relations is given for the general case.
Creation of Mass Processes and Perturbation Theory
Authors: Leviatan Talma
Published: December 2010

Creation of mass processes were treated lately by several authors. The idea was to find some generalized Markov process that will correspond to a semigroup of operators which are not necessarily contraction operators (or equivalently to a quasi transition function which is not submarkov). It was G. A. Hunt [6] who first suggested the idea of Markov processes in which both the starting time and the terminal time are random. Such processes were constructed by Helms [4] and treated also by Nagasawa [12] and the author [10].
Non-Linear A-Proper Mappings of the Analytic Type
Authors: Potter A. J. B.
Published: December 2010

Let Y be a complex Banach space, U an open subset of Y, f a mapping of U into Y. Then f is said to be complex analytic if for each pair of elements x and y of Y with x in U, the function f(x + ξy) of the single complex variable ξ is analytic in ξ on some neighbourhood of the origin.
Locally Convex Hypersurfaces
Authors: Jonker L. B. , Norman R. D.
Published: December 2010

Let M be an n-dimensional connected topological manifold. Let ξ : M → Rn+1 be a continuous map with the following property: to each x ∈ M there is an open set x ∈ Ux ⊂ M, and a convex body Kx ⊂ Rn+1 such that ξ(UX) is an open subset of ∂Kx and such that is a homeomorphism onto its image. We shall call such a mapping ξ a locally convex immersion and, along with Van Heijenoort [8] we shall call ξ(M) a locally convex hypersurface of Rn+1.
A Characterization of the Finite Simple Group PSp4(3)
Authors: Hayden John L.
Published: December 2010

The aim of this paper is to characterize the finite simple group PSp4(3) by the structure of the centralizer of an element of order three contained in the center of its Sylow 3-subgroup. More precisely, we shall prove the following results.
A Ratio Limit Theorem for Approximate Martingales
Authors: Lamb Charles W.
Published: December 2010

It has been proved [3, p. 630] that the martingale convergence theorem obtained by Andersen and Jessen [1, p. 5] follows from the classical theory developed by Doob. By using some results of Yosida and Hewitt [9] on finitely additive set functions, Johansen and Karush [7] proved that the identification of the limit function as a derivative in the approach of Andersen and Jessen can be obtained in the general case. In this paper we sharpen the methods of Andersen and Jessen to obtain a ratio limit theorem for “approximate martingales”.
Prime Ideals in Regular Self-Injective Rings
Authors: Goodearl K. R.
Published: December 2010

Although the notion of the maximal quotient ring of a nonsingular ring has been around for some time, not much is known about its structure in general beyond the important theorems of Johnson and Utumi [4; 11] that it is von Neumann regular and self-injective. The purpose of this paper is to study the structure of such a regular, self-injective ring R by looking at its prime ideals. Initially, we show that the primes of R separate into two types, called ‘'essential” and ‘“closed”, and that for any prime P, the two-sided ideals in the ring R/P are linearly ordered.
Sur Les Anneaux de Groupes Semi-Parfaits
Authors: Goursaud J. M.
Published: December 2010

Soient A un anneau unitaire, G un groupe. L'anneau de groupe AG est le A-module libre ayant pour base les éléments de G, la multiplication étant définie par :

avec

Le premier résultat de cet article concerne les annulateurs des idéaux à gauche engendrés par les sous-groupes finis de G, il permet d'obtenir une démonstration facile de la caractérisation des anneaux de groupes parfaits à gauche.
Chromatic Sums for Rooted Planar Triangulations, IV: The Case λ = ∞
Authors: Tutte W. T.
Published: December 2010

The chromial P(M, λ) of a planar near-triangulation M has the leading term λv(M), where v(M) is the number of vertices of M. The problem of finding the number of rooted planar near-triangulations of a given class S, all supposed to have the same number of vertices, can be regarded as a special case of the problem of finding chromatic sums. We can sum P(M, λ) over the members of S, divide by the appropriate power of λ and let λ → ∞. We thus get the sum of the coefficient of the leading term of P(M, λ) for all M ∈ S, that is we get the number of members of S.
Non-Metrizable Uniformities and Proximities on Metrizable Spaces
Authors: Sharma P. L.
Published: December 2010

In the literature there exist examples of metrizable spaces admitting nonmetrizable uniformities (e.g., see [3, Problem C, p. 204]). In this paper, this phenomenon is presented more coherently by showing that every non-compact metrizable space admits at least one non-metrizable proximity and uncountably many non-metrizable uniformities. It is also proved that the finest compatible uniformity (proximity) on a non-compact non-semidiscrete space is always non-metrizable.
Curvature and Radius of Curvature for Functions with Bounded Boundary Rotation
Authors: Noonan J. W.
Published: December 2010

For k ≧ 2 denote by Vk the class of functions f regular in and having the representation

(1.1)

where μ is a real-valued function of bounded variation on [0, 2π] with

(1.2)

Vk is the class of functions with boundary rotation at most kπ.
On Multiplicative Properties of Families of Complexes of Certain Loops
Authors: Steinberger Meir
Published: December 2010

It is well-known that if is a quotient group of a group G, then (i) is a partition of G, and (ii) the usual complex product (in the usual sense of multiplication of complexes) of every pair of members of is a member of . There arises the question whether, conversely, (i) and (ii), perhaps in a weaker form, suffice for to be a quotient group of G.
Conformally Flat Spaces of Codimension 2 in a Euclidean Space
Authors: Chen Bang-Yen , Yano Kentaro
Published: December 2010

In a previous paper [1], the authors introduced and studied the notion of special conformally flat spaces and quasi-umbilical hypersurfaces. In that paper, the authors proved that every conformally flat space of codimension one in a Euclidean space is special and, conversely, every special conformally flat space can be isometrically immersed in a Euclidean space as a quasi-umbilical hypersurface.

In the present paper, the authors study the conformally flat spaces of codimension 2 in a Euclidean space. (Manifolds, mappings, functions, etc. are assumed to be sufficiently differentiate and we shall restrict ourselves only to manifolds of dimension n > 3.)