bluuebunny/crossref_metadata_2025_split huggingface dataset:
Tensor Products and the Splitting of Abelian Groups
Authors: Lawver D. A. , Toubassi E. H. 
Published: December 2010

In [2], Irwin, Khabbaz, and Rayna discuss the splitting problem for abelian groups through the use of the tensor product. Throughout the paper they make a basic assumption, namely, that the torsion subgroup contains but one primary component. Under this restriction they introduce the concept of “splitting length”, which is a positive integer indicator of how far a group is from splitting. The results obtained along these lines may be extended to groups whose torsion subgroups contain any finite number of primary components by applying the work of Oppelt [4].Irwin, Khabbaz, and Rayna [2] define the notion of a p-sequence and show that for groups A where T(A) is p-primary and A/T(A) has rank one, the existence of a torsion-free element with a p-sequence is sufficient for the group to split.
The Lattice of Equational Classes of Commutative Semigroups
Authors: Nelson Evelyn 
Published: December 2010

There has been some interest lately in equational classes of commutative semigroups (see, for example, [2; 4; 7; 8]). The atoms of the lattice of equational classes of commutative semigroups have been known for some time [5]. Perkins [6] has shown that each equational class of commutative semigroups is finitely based. Recently, Schwabauer [7; 8] proved that the lattice is not modular, and described a distributive sublattice of the lattice.The present paper describes a “skeleton” sublattice of the lattice, which is isomorphic to A × N+ with a unit adjoined, where A is the lattice of pairs (r, s) of non-negative integers with r ≦ s and s ≧ 1, ordered component-wise, and N+ is the natural numbers with division.
Weierstrass Points at the Cusps of Γ0(16p) and Hyperellipticity of Γ0(n)
Authors: Larcher H. 
Published: December 2010

For a fixed positive integer n we consider the subgroup Γ0(n) of the modular group Γ(l). Γ0(n) consists of all linear fractional transformations L: z → (az + b)/(cz + d) with rational integers a, b, c, d, determinant ad – bc = 1, and c ≡ 0(mod n). If ℋ = {z|z = x + iy, x and y real and y > 0} is the upper half of the z-plane then S0 = S0(n) = ℋ/Γ0(n), properly compactified, is a compact Riemann surface whose genus we denote by g(n). A point P of a Riemann surface S of genus g is called a Weierstrass point if there exists a function on S that has a pole of order α ≦ g at P and is regular everywhere else on S.Lehner and Newman started the search for Weierstrass points of S0 (or, loosely, of Γ0(n)).
Extreme Points in the Hardy Class H1 of a Riemann Surface
Authors: Pranger Walter 
Published: December 2010

The theorems presented here extend known results on the set of extreme points of the unit ball of the Hardy class H1 of a disk to the situation of an arbitrary Riemann surface. Several new results are obtained. The initial motivation for this work was provided by the theorem of de Leeuw and Rudin [2, p. 471] characterizing the extreme points in the case ol a disk. Careful scrutiny of the proof of that theorem yields one necessary and one sufficient condition for being an extreme point in H1 of an arbitrary surface (Theorems 1 and 4 below). The material presented here on compact bordered surfaces is closely related to the beautiful results of Gamelin and Voichick [4] and the results of Forelli [3].For a subharmonic function u, which has a harmonic majorant on the Riemann surface R, Mu will denote the least harmonic majorant of u.
A Class of Non-Central E-Functors
Authors: Chapman G. R. 
Published: December 2010

We refer the reader to [1, Chapters 1 and 2] for the notions of E-functor and centrality. Let R1 ⊆ R be the integral group rings of the groups G1⊆ G. Butler and Horrocks [1, Chapter 26] have shown that on the category of left, unitary R-modules the Hochschild E-functor determined by R1 is central. There are no examples of non-central Hochschild E-functors, and our purpose is to establish the existence of a class of such E-functors.Take G to be finite, non-abelian and let 5 be the centre of R. Denote by φ the Hochschild E-functor determined by S. We obtain a necessary condition for the centrality of φ in terms of the group structure of G. Let G* denote the subgroup of G generated by the commutators of G together with the set ﹛gh(g): g £ G﹜, where h(g) is the class number of g in G.
Generalization of Watson's Lemma
Authors: Wong R. , Wyman M. 
Published: December 2010

Many functions, F(z), have integral representations of the form1.1the so-called Laplace transform of f(t). When f(t) satisfies certain regularity conditions, it is possible to use Cauchy's theorem to deform the contour so that F(z) has the integral representation1.2where 7 is a fixed real number, and the path of integration is the straight line joining t = 0 to t = ∞ etr, small indentations in the path of integration being allowed to avoid singularities of f(t) where necessary. When the two functions defined by (1.1) and (1.2) are not the same, (1.2) provides the more general situation for a theoretical discussion of the properties of F(z).
Extensions of One Primitive Inverse Semigroup by Another
Authors: Ault Janet E. 
Published: December 2010

Every inverse semigroup containing a primitive idempotent is an ideal extension of a primitive inverse semigroup by another inverse semigroup. Consequently, in developing the theory of inverse semigroups, it is natural to study ideal extensions of primitive inverse semigroups (cf. [3; 7]). Since the structure of any primitive inverse semigroup is known, an obvious type of ideal extension to consider is that of one primitive inverse semigroup by another. In this paper, we will construct all such extensions and give an abstract characterization of the resulting semigroup.The problem of extending one primitive inverse semigroup by another can be essentially reduced to that of extending one Brandt semigroup by another Brandt semigroup. The latter problem has been solved by Lallement and Petrich in [3] in case the first Brandt semigroup has only a finite number of idempotents.
Two R-Closed Spaces
Authors: Stephenson R. M. 
Published: December 2010

Throughout this paper all hypothesized spaces are T1. A regular space is called R-closed[11](regular-closed [7] or, equivalently, regular-complete [2]) provided that it is a closed subset of any regular space in which it can be embedded. A regular space (X, ℐ) is called minimal regular [2; 4] if there exists no regular topology on X which is strictly weaker than J. We shall call a regular space X strongly minimal regular provided that each point x ∈ X has a fundamental system of neighbourhoods such that for every V ∈ , X\V is an R-closed space.In §2 we note that a strongly minimal regular space is minimal regular, but we do not know if the converse holds. M. P. Berri and R. H. Sorgenfrey [4] proved that a minimal regular space is R-closed, and Horst Herrlich [7] gave an example of an R-closed space that is not minimal regular.
Varieties of Orthomodular Lattices. II
Authors: Bruns Günter , Kalmbach Gudrun 
Published: December 2010

In this paper we continue the study of equationally defined classes of orthomodular lattices started in [1].The only atom in the lattice of varieties of orthomodular lattices is the variety of all Boolean algebras. Every nontrivial variety contains it. It follows from B. Jónsson [4, Corollary 3.2] that the variety [MO2] generated by the orthomodular lattice MO2 of Figure 1 covers the variety of all Boolean algebras. I t was first shown by R. J. Greechie (oral communication) and is not difficult to see that every variety not consisting of Boolean algebras only contains [MO2]. Again it follows from the result of Jónsson's mentioned above that the varieties generated by one of the orthomodular lattices of Figures 2 to 5 cover [MO2]. The Figures 4 and 5 are to be understood in such a way that the orthocomplement of every element is on the vertical line through this element.
Higher Monotonicity Properties of Certain Sturm-Liouville Functions. IV
Authors: Lorch Lee , Muldoon Martin E. , Szego Peter 
Published: December 2010

The Sturm-Liouville functions considered in this instalment are real (as are all other quantities discussed here) non-trivial solutions of the differential equation1.1Higher monotonicity properties, as defined in § 2, are investigated for a number of sequences (finite or infinite) associated with these functions. One such sequence, discussed in detail later, has the kth term1.2where the constant X > — 1 (to assure convergence of each integral), W(x) possesses higher monotonicity properties and, moreover, is such that, again, each integral converges, and X1, X2, … is a sequence (finite or infinite) of consecutive zeros of a solution of (1.1), which may or may not be linearly independent of y(x), in the interval of definition of the functions under consideration.
On Strong Nörlund Summability Fields
Authors: Kuttner Brian , Thorpe Brian 
Published: December 2010

Let p denote the sequence {pn} and set wherever this series converges. (Where no limits are stated, sums are throughout to be taken from n = 0 to n = ∞.) We use a similar notation with other letters in place of p. Given two sequences p, q, the convolution p*q is defined byit is familiar, and easily verified, that the operation of convolution is commutative and associative. We write Pn = (p*l)n (where 1 denotes the sequence {1} ), and take P-1 to mean 0. If, for all n ≦ 0, Pn ≠ 0, then we define the Nörlund mean (N, p) of the sequence s as σn, whereand (σ-1 = 0. If σn → λ as n → ∞, then 5 is said to be limitable (N, p) to the number λ
Positive Linear Maps on C*-Algebras
Authors: Choi Man-Duen 
Published: December 2010

The objective of this paper is to give some concrete distinctions between positive linear maps and completely positive linear maps on C*-algebras of operators.Herein, C*-algebras possess an identity and are written in German type . Capital letters A, B, C stand for operators, script letters for vector spaces, small letters x, y, z for vectors. Capital Greek letters Φ, Ψ stand for linear maps on C*-algebras, small Greek letters α, β, γ for complex numbers.We denote by the collection of all n × n complex matrices. () = ⊗ is the C*-algebra of n × n matrices over .
Rings with Finite Norm Property
Authors: Levitz Kathleen B. , Mott Joe L. 
Published: December 2010

A ring A has finite norm properly,
abbreviated FNP, if each proper homomorphic image of
A is finite. In [3], Chew and Lawn
described some of the structural properties of FNP rings
with identity, which they called residually finite rings. The twofold aim of
this paper is to extend the results of [3] to arbitrary rings
with FNP and to give characterizations of
FNP rings independent of the results of
[3].If A is a ring, let A+ denote A regarded as an abelian group. In the
first section of this paper, we explore the effects of FNP
upon the structure of A+. The following theorem
is typical of the results in this section.
Galois Theory of Essential Extensions of Modules
Authors: Wiegand Sylvia 
Published: December 2010

The purpose of this paper is to exploit an analogy between algebraic
extensions of fields and essential extensions of modules, in which the role
of the algebraic closure of a field F is played by the
injective hull H(M) of a unitary left
R-module M. (The notion of * ‘algebraic’
extensions of general algebraic systems has been studied by Shoda; see, for
example [5].)In this analogy, the role of a polynomial p(x) is played by
a homomorphism of R-modules(1)which will be called an ideal homomorphism into
M. The process of solving the equation
p(x) = 0 in F, or in an algebraic
extension of F, will be replaced by the process of
extending an ideal homomorphism (1) to a homomorphism
F* from R into M, or into an
essential extension of M.
Normed Lie Algebras
Authors: Vasilescu F.-H. 
Published: December 2010

In this paper we attempt to define the notion of normed Lie algebra by
endowing the corresponding algebraic concept with topologicalmetric
properties. More precisely, we define normed Lie algebras as being normed
spaces possessing a Lie product, the latter satisfying a compatibility
relation. It turns out that any normed algebra, in particular the algebra of
continuous linear operators on a normed space, is a normed Lie algebra in
the sense denned below, with the usual Lie product given by the additive
commutator.It seems that some algebraic features have within the framework of normed
Lie algebras the natural topological extensions. We mention, for instance,
the convergence of the well-known Campbell-Hausdorff formula. Let us also
mention the occurence of a variant of the Kleinecke-Sirokov theorem,
obtained via universal enveloping algebra, which might be unknown in this
context.
Abelian Groups Quasi-Injective Over their Endomorphism
Rings
Authors: Poole George D. , Reid James D. 
Published: December 2010

L. Fuchs has posed the problem of identifying those abelian
groups that can serve as the additive structure of an injective module over
some ring [1, p. 179], and in particular of identifying those
abelian groups which are injective as modules over their endomorphism rings
[1, p. 112]. Richman and Walker have recently answered the
latter question, generalized in a non-trivial way [7], and have
shown that the groups in question are of a rather restricted structure.In this paper we consider abelian groups which are quasi-injective over
their endomorphism rings. We show that divisible groups are quasi-injective
as are direct sums of cyclic p-groups. Quasi-injectivity of
certain direct sums (products) is characterized in terms of the summands
(factors). In general it seems that the answer to the question of whether or
not a group G is quasinjective over its endomorphism ring
E depends on how big HomE(H,
G) is, with H a fully invariant subgroup of
G.
On the Ring of Quotients at a Prime Ideal of a Right Noetherian
Ring
Authors: Heinicke A. G. 
Published: December 2010

J. Lambek and G. Michler [3] have initiated the study of a ring
of quotients RP associated with a two-sided prime ideal P in a
right noetherian ring R. The ring RP is the quotient ring (in the sense of [1]) associated
with the hereditary torsion class τ consisting of all right R-modules
M for which HomR(M, ER(R/P)) = 0, where ER(X) is the injective hull of the R-module
X.In the present paper, we shall study further the properties of the ring
RP. The main results are Theorems 4.3 and
4.6. Theorem 4.3 gives necessary and sufficient conditions for the torsion
class associated with P to have property
(T), as well as some properties of RP when these conditions are indeed satisfied, while Theorem 4.6
gives necessary and sufficient conditions for R to satisfy
the right Ore condition with respect to (P).
An Embedding Theorem for Ordered Groups
Authors: Minassian Donald P. 
Published: December 2010

An O*-group is a group wherein every partial
order can be extended to some full order.THEOREM. Suppose the group G has a normal chain G = G1 ⊇ G2 ⊇ … such thatand each G/Gi is locally nilpotent and torsion-free. Then
G can be embedded in thecomplete direct product G’ of divisible
O*-groups.
An Lp Saturation Theorem for Splines
Authors: Butler G. J. , Richards F. B. 
Published: December 2010

Let 1 be a
subdivision of [0, 1], and let denote the
class of functions whose restriction to each sub-interval is a polynomial of degree at most
k. Gaier [1] has shown that for uniform
subdivisions △n (that is, subdivisions for which if and only if f is a polynomial of degree at most
k. Here, and subsequently, denotes the usual norm in Lp[0,
1], 1 ≦ p ≦ ∞, and we should
emphasize that functions differing only on a set of Lebesgue measure zero
are identified.
Graphical Regular Representations of Non-Abelian Groups, II
Authors: Nowitz Lewis A. , Watkins Mark E. 
Published: December 2010

The present paper is a sequel to the previous paper bearing the same title by the same authors [3] and which will be hereafter designated by the bold-face Roman numeral I. Further results are obtained in determining whether a given finite non-abelian group G has a graphical regular representation. In particular, an affirmative answer will be given if (|G|, 6) = 1.Inasmuch as much of the machinery of I will be required in the proofs to be presented and a perusal of I is strongly recommended to set the stage and provide motivation for this paper, an independent and redundant introduction will be omitted in the interest of economy.
𝔪-Stone Lattices
Authors: Davey B. A. 
Published: December 2010

A Stone lattice is a distributive, pseudo-complemented lattice L such that a* V a** = 1, for all a in L; or equivalently, a bounded distributive lattice L in which, for all a in L, the annihilator a⊥ = {b ∊ L|a ∧ b = 0} is a principal ideal generated by an element of the centre of L, namely a*.Thus it is natural to define an 𝔪-Stone lattice to be a bounded distributive lattice L in which, for each subset A of cardinality less than or equal to m, the annihilator A⊥ = {b ∊ L|a ∧ b = 0, for all a ∊ A} is a principal ideal generated by an element of the centre of L.In this paper we characterize 𝔪-Stone lattices, and show, by considering the lattice of global sections of an appropriate sheaf, that any bounded distributive lattice can be embedded in an 𝔪-Stone lattice, the embedding being a left adjoint to the forgetful functor.
A Theorem on Isometries and the Application of it to the Isometries of Hp(S) for 2 < p < ∞
Authors: Forelli Frank 
Published: December 2010

Let X and Y be sets, let λ be a bounded positive measure on X, and let μ be a bounded positive measure on Y. Furthermore let M be a subalgebra of L∞(λ), let p ∈ (0, ∞), and let A be a linear transformation of M into Lp(μ) such thatfor all f in M.In § 2 of this paper we will prove the following theorem.
Generalizations of Noshiro's Theorem and Their Applications
Authors: Yoshida Hidenobu 
Published: December 2010

Meier [8, Hauptsatz] proved a remarkable theorem concerning the boundary behavior of functions meromorphic in the upper half plane; but his techniques are very complicated. So Noshiro [10, p. 72-73] proved an analogous (but somewhat weaker) result to Meier's by a simple method using the theorem of Gross and Iversen.In this paper, we sharpen and generalize Noshiro's theorem in some directions by making use of the notion “porosity”, and we state some applications.
A Note on Root Decision Problems in Groups
Authors: Lipschutz Seymour , Lipschutz Martin 
Published: December 2010

Consider a positive integer r > 1. We say that the rth root problem is solvable for a group G if we can decide for any W ॉ G whether or not W has an rth root, i.e. whether or not there exists V ॉ G such that W = Vr.Baumslag, Boone and Neumann [1] proved that there exists a finitely presented group with all root problems unsolvable. Here we are concerned with the relationship between the different root problems.
Algebras Over Dedekind Domains
Authors: Wehlen Joseph A. 
Published: December 2010

The purpose of this paper is two-fold : first, to show that Dedekind domains satisfy a generalization of the Wedderburn-Mal'cev Theorem and, secondly, to classify certain types of finitely generated projective algebras over a Dedekind domain.With respect to the first problem, E. C. Ingraham has shown that a Dedekind domain R is an inertial coefficient ring (IC-ring) if and only if R has zero radical or R is a local Hensel ring.
On Hereditary and Cohereditary Modules
Authors: Shrikhande M. S. 
Published: December 2010

A recent paper by Goro Azumaya on M-projective and M-injective modules [1] suggests a generalization of the concept of hereditary rings to modules which is also capable of dualization. Section 2 is devoted to preliminaries on M-projective and M-infective modules.In section 3, we introduce the notion of hereditary and cohereditary modules. An R-module is called hereditary if every R-submodule of it is projective. Cohereditary modules are defined dually.
An Improved Subgroup Theorem for HNN Groups with Some Applications
Authors: Karrass A. , Pietrowski A. , Solitar D. 
Published: December 2010

In [4], a subgroup theorem for HNN groups was established. The theorem was proved by embedding the given HNN group in a free product with amalgamated subgroup and then applying the subgroup theorem of [3]. In this paper we obtain a sharper form of the subgroup theorem of [4] by applying the Reidemeister-Schreier method directly, using an appropriate Schreier system of coset representatives. Specifically, we prove (in Theorem 1) that if H is a subgroup of the HNN group1
Combinatorial Properties of Associated Zonotopes
Authors: Shephard G. C. 
Published: December 2010

Let S
1 . . . ,Sr
be r line segments, each of non-zero
length, in n-dimensional euclidean space R
n
. If a polytope Z is defined as the vector
(Minkowski) sum
(1) Z = S
1 + . . . + Sr
,
then the segments Si
will be called the components of
Z. Since we do not wish to exclude the possibility
that some of the components may be parallel, the polytope
Z may be written in the form (1) in many different
ways. For this reason it is convenient to define a
zonotope to be the polytope
Z together with some specified set of components {S1
, . . . , Sr
}. Figures 1, 2 and 3 show some zonotopes of 1, 2 and 3 dimensions
with 4, 5 and 6 components.
On Algebras Generated by Composition Operators
Authors: Cima J. A. , Wogen W. R. 
Published: December 2010

Let Δ be the open unit disk in the complex plane and let be the group of automorphisms of Δ onto Δ, define byThe Banach spaces Hp = Hp(Δ), 1 ≦ p < ∞, are the Hardy spaces of functions analytic in Δ with their integral p means bounded,
On Some Complex Submanifolds in Kaehler Manifolds
Authors: Kon Masahiro 
Published: December 2010

The purpose of this paper is to give some conditions for complex submanifolds in a Kaehler manifold of constant holomorphic sectional curvature to be Einstein.For a complex hypersurface which is Einstein, Smyth [8] has obtained its classification and Chern [2] has proved the corresponding local result. Moreover, Takahashi [9] and Nomizu-Smyth [3] generalized this to a complex hypersurface with parallel Ricci tensor. We shall consider a condition weaker than the requirement that the Ricci tensor be parallel, that is we shall consider a complex submanifold with commuting curvature and Ricci operator, which condition was treated by Bishop-Goldberg [1].
A Characteristic Subgroup of π-Stable Groups
Authors: Arad Zvi 
Published: December 2010

All groups in this paper are assumed to be finite.Let G be a group with op(G) ≠ 1 which is p-constrained and p-stable, p odd. If P is an Sp-subgroup of G, then by Glaubermaris Theorem, [3, 8.2.11],G = Op′(G)NG(ZJ(P)).
Absolute Purity
Authors: Fieldhouse David J. 
Published: December 2010

Throughout this paper we use the Bourbaki [1] conventions for rings and modules: all rings are associative but not necessarily commutative and have a 1; all modules are unital.Our purpose is to extend and simplify some recent results of Maddox [7], Megibben [8], Enochs [3], and the author [5] on absolutely pure modules by introducing several new dimensions, and using the absolutely pure dimension introduced by the author in [6], This completes some work on character modules and dimension in [5] and [6].An A -module will be called an FFR-module if and only if it has a resolution by finitely generated free A -modules.
Unit Preserving Isometries are Homomorphisms in Certain Lp
Authors: Schneider Robert 
Published: December 2010

(a) (ᓂ1 and ᓂ2 will always denote positive bounded measures of equal mass defined on sets X and F respectively. Lp(ᓂ1) and Lp(ᓂ2) will always be complex Lp spaces.(b) M C L∞(ᓂ1) will always denote a subalgebra of L∞(ᓂ1) containing constants.(c) Let be a 1 inear map of ikf into Lp(ᓂ2). We shall say that T is a linear isometry in LP norm ifWe shall prove the following:THEOREM B. If 2 < p < ∞ and is a linear isometry in the Lp norm with T(l) = 1 then T is a homomorphism on M; that is