bluuebunny/crossref_metadata_2025 huggingface dataset:
Digraphs and the semigroup of all functions on a finite set
Authors: Higgins Peter M.
Published: May 2009

Let Tn denote the full transformation semigroup on the finite set = {1, 2, … n}, that is the set of all mappings from to , with function composition as the semigroup operation. In this paper algorithms are introduced to solve equations such as axmb = c and ax = xb (a, b, c ∊ Tn), which employ a representation of members of Tn as special directed graphs.
A characterization of artinian rings
Authors: van Huynh Dinh , Dung Nguyen V.
Published: May 2009

Throughout this paper we consider associative rings with identity and assume that all modules are unitary. As is well known, cyclic modules play an important role in ring theory. Many nice properties of rings can be characterized by their cyclic modules, even by their simple modules. See, for example, [2], [3], [6], [7], [13], [14], [15], [16], [18], [21]. One of the most important results in this direction is the result of Osofsky [14, Theorem] which says: a ring R is semisimple (i.e. right artinian with zero Jacobson radical) if and only if every cyclic right R-module is injective. The other one is due to Vamos [18]: a ring R is right artinian if and only if every cyclic right R-module is finitely embedded.
Spinors and canonical hermitian forms
Authors: Robinson P. L.
Published: May 2009

The spaceSof spinors associated to a2m-dimensional real inner product space (V, B) carries a canonical Hermitian form 〈 〉 determined uniquely up to real multiples. This form arises as follows: the complex Clifford algebraC(V) of (V, B) is naturally provided with an antilinear involution; this induces an involution on EndSvia the spin representation; this is the adjoint operation corresponding to 〈 〉.
Elementary operators on prime C*-algebras II
Authors: Mathieu Martin
Published: May 2009

Compact elementary operators acting on the algebra ℒ(H) of all bounded operators on some Hilbert space H were characterised by Fong and Sourour in [9]. Akemann and Wright investigated compact and weakly compact derivations on C*-algebras [1], and also studied compactness properties of the sum and the product of the right and the left regular representation of an element in a C*-algebra [2]. They used the concept of a compact Banach algebra element due to Vala [17]: an element a in a Banach algebra A is called compact if the mapping x → axa is compact on A. This notion has been further investigated by Ylinen [18, 19, 20], who showed in particular that a is a compact element of the C*-algebra A if x ↦ axa is weakly compact on A [19].
The smallest proper congruence on S(X)
Authors: Hofmann K. H. , Magill K. D.
Published: May 2009

S(X) is the semigroup of all continuous self maps of the topological space X and for any semigroup S, Cong(S) will denote the complete lattice of congruences on S. Cong(S) has a zero Z and a unit U. Specifically, Z = {(a, a):a ∈ S} and U = S × S. Evidently, Z and U are distinct if S has at least two elements. By a proper congruence on S we mean any congruence which differs from each of these. Since S(X) has more than one element when X is nondegenerate, we will assume without further mention that the spaces we discuss in this paper have more than one point. We observed in [4] that there are a number of topological spaces X such that S(X) has a largest proper congruence, that is, Cong(S(X)) has a unique dual atom which is greater than every other proper congruence on S(X). On the other hand, we also found out in [5] that it is also common for S(X) to fail to have a largest proper congruence. We will see that the situation is quite different at the other end of the spectrum in that it is rather rare for S(X) not to have a smallest proper congruence. In other words, for most spaces X, Cong(S(X)) has a unique atom which is smaller than every other proper congruence.
On the product of all nonzero elements of a finite ring
Authors: Hermann Peter Z.
Published: May 2009

The aim of the present note is to describe the possible products when taking all the nonzero elements of a finite ring in some sequence. Compared with the analogous situation for finite groups, where the set of products of all elements has been shown in [2] to be a whole coset of the derived group, for rings the set of the above mentioned products will be proved either to be as large as possible or to consist of one or two elements only.
Equational bases for subvarieties of double MS-algebras
Authors: Blyth T. S. , Noor A. S. A. , Varlet J. C.
Published: May 2009

An MS-algebra is an algebra (L; ∨, ∧, ∘, 0, 1) of type (2, 2, 1, 0, 0) such that (L; ∨, ∧, 0, 1) is a distributive lattice with smallest element 0 and greatest element 1, and x ↦ x∘ is a unary operation such that l∘ = 0, x ≤ x∘∘ for all x ∈ L, and (x ∧ y)∘ = x∘ ∨ y∘ for all x, y ∈ L. These algebras belong to the class of Ockham algebras introduced by Berman [3]; see also [2,10,15]. A double MS-algebra is an algebra (L, ∨, ∧, ∘, +, 0, 1) of type (2, 2, 1, 1, 0, 0) such that (L, ∘) and (Ld, +) are MS-algebras, where Ld denotes the dual of L, and the operations ∘, + are linked by the identities x∘+ = x∘∘ and x+∘ = x++. We refer to [5, 6, 7, 8] for the basic properties of MS-algebras and double MS-algebras. Concerning the latter, the properties x∘∘∘ = x∘, x+++ = x+, and x∘ ≤ x+will be used frequently. The class of double MS-algebras is congruencedistributive and consequently the results of [13] can be applied. As to general results in lattice theory and universal algebra, the reader may consult [1, 9, 12].
The non-abelian tensor product of groups and related constructions
Authors: Gilbert N. D. , Higgins P. J.
Published: May 2009

The tensor product of two arbitrary groups acting on each other was introduced by R. Brown and J.-L. Loday in [5, 6]. It arose from consideration of the pushout of crossed squares in connection with applications of a van Kampen theorem for crossed squares. Special cases of the product had previously been studied by A. S.-T. Lue [10] and R. K. Dennis [7]. The tensor product of crossed complexes was introduced by R. Brown and the second author [3] in connection with the fundamental crossed complex π(X) of a filtered space X, which also satisfies a van Kampen theorem. This tensor product provides an algebraic description of the crossed complex π(X ⊗ Y) and gives a symmetric monoidal closed structure to the category of crossed complexes (over groupoids). Both constructions involve non-abelian bilinearity conditions which are versions of standard identities between group commutators. Since any group can be viewed as a crossed complex of rank 1, a close relationship might be expected between the two products. One purpose of this paper is to display the direct connections that exist between them and to clarify their differences.
On weak approximation and convexification in weighted spaces of vector-valued continuous functions
Authors: Nawrocki Marek
Published: May 2009

Let X be a completely regular Hausdorff space. A Nachbin family of weights is a set V of upper-semicontinuous positive functions on X such that if u, υ ∈ V then there exists w ∈ V and t > 0 so that u, υ ≤ tw. For any Hausdorff topological vector space E, the weighted space CV0(X, E) is the space of all E-valued continuous functions f on X such that υf vanishes at infinity for all υ ∈ V. CV0(X, E) is equipped with the weighted topologywv = wv(X, E) which has as a base of neighbourhoods of zero the family of all sets of the form

where υ ∈ Vand W is a neighbourhood of zero in E. If E is the scalar field, then the space CV0(X, E) is denoted by CV0(X). The reader is referred to [4, 6, 8] for information on weighted spaces.
OnE-groups in the sense of Peng
Authors: Heineken Hermann
Published: May 2009

The groupsGof the title are those in whichEG(x) = {y|y∈G, [y,nx] = 1 for somen} is a subgroup for everyxinG.We show that the quotient groupG/F(G) is rather restricted for finiteE-groups; in particular, soluble finiteE-groups are of Fitting length 4 at most. Some criteria for infinite groups are given.
The semigroup of one-to-one transformations with finite defects
Authors: Levi Inessa , Schein Boris M.
Published: May 2009

Letbe the semigroup of all total one-to-one transformations of an infinite setX.For an ƒ ∈let thedefectofƒdefƒ, be the cardinality ofX – R(ƒ), whereR(ƒ) = ƒ(X) is the range of ƒ. Thenis a disjoint union of the symmetric groupxonX, the semigroupSof all transformations inwith finite non-zero defects and the semigroup Ā of all transformations inSwith infinite defects, such that S U Ā and Ā are ideals of. The properties ofxand Ā have been investigated by a number of authors (for the latter it was done via Baer-Levi semigroups, see [2], [3], [5], [6], [7], [8], [9], [10] and note that Ā decomposes into a union of Baer–Levi semigroups). Our aim here is to study the semigroupS.It is not difficult to see thatSis left cancellative (we compose functions ƒ,ginSas ƒg(x) = ƒ(g(x)), forx∈X) and idempotent-free. All automorphisms ofSare inner [4], that is of the form ƒ →hƒhfh-1ƒ ∈S,h∈x.
Rings characterized by cyclic modules
Authors: van Huynh Dinh , Dan Phan
Published: May 2009

A ring R is called right PCI if every proper cyclic right R-module is injective, i.e. if C is a cyclic right R-module then CR ≅ RR or CR is injective. By [2] and [3], if R is a non-artinian right PCI ring then R is a right hereditary right noetherian simple domain. Such a domain is called a right PCI domain. The existence of right PCI domains is guaranteed by an example given in [2]. As generalizations of right PCI rings, several classes of rings have been introduced and investigated, for example right CDPI rings, right CPOI rings (see [8], [6]). In Section 2 we define right PCS, right CPOS and right CPS rings and study the relationship between all these rings.
On Banach spaces with Mazur's property
Authors: Leung Denny H.
Published: May 2009

A Banach space E is said to have Mazur's property if every weak* sequentially continuous functional in E” is weak* continuous, i.e. belongs to E. Such spaces were investigated in [5] and [9] where they were called d-complete and μB-spaces respectively. The class of Banach spaces with Mazur's property includes the WCG spaces and, more generally, the Banach spaces with weak* angelic dual balls [4, p. 564]. Also, it is easy to see that Mazur's property is inherited by closed subspaces. The main goal of this paper is to present generalizations of some results of [5] concerning the stability of Mazur's property with respect to forming some tensor products of Banach spaces. In particular, we show in Sections 2 and 3 that the spaces E ⊗εF and Lp(μ, E) inherit Mazur's property from E andF under some conditions. In Section 4, we will also show the stability of Mazur's property under the formation of Schauder decompositions and some unconditional sums of Banach spaces.
Free right type A semigroups
Authors: Fountain John
Published: May 2009

The relation ℒ* is defined on a semigroup S by the rule that a ℒ*b if and only if the elements a, b of S are related by Green's relation ℒ in some oversemigroup of S. A semigroup S is an E-semigroup if its set E(S) of idempotents is a subsemilattice of S. A right adequate semigroup is an E-semigroup in which every ℒ*-class contains an idempotent. It is easy to see that, in fact, each ℒ*-class of a right adequate semigroup contains a unique idempotent [8]. We denote the idempotent in the ℒ*-class of a by a*. Then we may regard a right adequate semigroup as an algebra with a binary operation of multiplication and a unary operation *. We will refer to such algebras as *-semigroups. In [10], it is observed that viewed in this way the class of right adequate semigroups is a quasi-variety.
The equation y′ = fy in zero residue characteristic
Authors: Escassut Alain , Sarmant Marie-Claude
Published: May 2009

Let K be an algebraically closed field complete with respect to an ultrametric absolute value |.| and let k be its residue class field. We assume k to have characteristic zero (hence K has characteristic zero too).

Let D be a clopen bounded infraconnected set [3] in K, let R(D) be the algebra of the rational functions with no pole in D, let ‖.‖D be the norm of uniform convergence on D defined on R(D), and let H(D) be the algebra of the analytic elements on D i.e. the completion of R(D) for the norm ‖.‖D.
Toeplitz operators and algebras of bounded analytic functions on the disk
Authors: Smith R. C.
Published: May 2009

Here and throughout, A is a closed subalgebra of H∞ that contains the disk algebra and M(A) denotes the maximal ideal space of A. Because A contains the function fo(z) = z, we can define the fiber Mλ(A) of M(A) for λ ε ∂D (the unit circle) in the usual way; i.e., Mλ(A) = {φ ∈ M(A): fo(φ) = λ}. The Bergman space of the unit disk D is the L2(D, dx dy)-closure of A. Let be the orthogonal projection. For f ∈ L∞(D, dx dy), define the multiplication operator Mf: L2(D, dx dy)→ L2, (D, dx dy) by

and define the Toeplitz operator by
Characterisations of partially continuous, strictly cosingular and φ- type operators
Authors: Labuschagne L. E.
Published: May 2009

We will denote the dimension of a subspace M of X by dim M and the codimension of M with respect to X by codxM or simply cod M if there is no danger of confusion. The classes of infinite dimensional and closed infinite codimensional subspaces of X will be denoted by and respectively with ℱ(X) and ℱ(X) denoting the classes of finite dimensional and of finite codimensional subspaces of X respectively. For a subspace M of X we denote the injection of M into X by and the quotient map from X onto the quotient space X/M by . Where there is no danger of confusion we will write JM and QM. The injection of X into its completion will be denoted by Jx. Letting X′ denote the continuous dual of X we remark that since X′ is isometric to ()′, these two spaces will be considered identical where convenient. The orthogonal complements of subsets M ⊂ X in X′ and K ⊂ X′ in X will be denoted by M⊥ and ⊥K respectively; M⊥X and X⊥K will be used if there is danger of confusion.
Functional iteration and the Josephus problem
Authors: Odlyzko Andrew M. , Wilf Herbert S.
Published: May 2009

The problem of Josephus is the following. We are given two positive integers n, q. There are n places arranged around a circle, and numbered clockwise 1, 2, …, n. Each of n people takes one of the places, then (please excuse this, but we didn't invent the problem!) every qth one is executed, until just one remains. More precisely, the occupant of place q is ‘removed’ first, and in general, if some place j has just been vacated, then the qth one of the places clockwise around from j that are still occupied will be vacated next. One question is this: if you would like to be the last survivor, then into what place should you go initially? We denote the answer to this question by Jq(n). For example, if n = 5 and q = 2, the order of execution is 2, 4, 1, 5, 3, and J2(5) = 3. Other questions have been raised about the problem, and it has an extensive literature (see [1]–[10]). In this paper we deal with the Jq(n)'s.
Projective structures on an annulus and Hankel forms
Authors: Peetre Jaak , Zhang Genkai
Published: May 2009

A general theory of Hankel forms over domains in one or several variables has been set forth in [6]. In [7] the study of Hankel forms over an annulus in the complex plane ℂ was begun. (An extension of the results of [7] to multiply connected domains was given in [4].) The present paper amplifies the results of [7] in various respects. First of all we define and study more general Hankel forms associated with a one parameter family of projective structures on the annulus. This displays several new features. For instance, we are now dealing with quadratic integral metrics which do not correspond to integration of the square of the function with respect to a weight. Furthermore, whereas in [7] essentially only the issue of the boundedness of Hankel forms was studied, we obtain here rather satisfactory Sp-results, even for 0 < p < 1. The question which remains is, of course, to which extent all this extends to multiply connected domains (or more general (open) Riemann surfaces).
An embedding for π2of a subcomplex of a finite contractible two-complex
Authors: Bogley William A.
Published: May 2009

A longstanding open question in low dimensional topology was raised by J. H. C. Whitehead in 1941 [9]: “Is any subcomplex of an aspherical, two-dimensional complex itself aspherical?” The asphericity of classical knot complements [7] provides evidence that the answer to Whitehead's question might be “yes”. Indeed, each classical knot complement has the homotopy type of a two-complex which can be embedded in a finite contractible two-complex. This property is shared by a large class of four-manifolds; these are the ribbon disc complements, whose asphericity has been conjectured, and even claimed, but never proven. (See [4] for a discussion.) It is reasonable and convenient to formulate the following.
Interpolating sequences for the derivatives of Bloch functions
Authors: Attele K. R. M.
Published: May 2009

We prove that sufficiently separated sequences are interpolating sequences for f′(z)(1−|z|2) where f is a Bloch function. If the sequence {zn} is an η net then the boundedness f′(z)(1−|z|2) on {zn} is a sufficient condition for f to be a Bloch function. The essential norm of a Hankel operator with a conjugate analytic symbol acting on the Bergman space is shown to be equivalent to .
Constructing quaternionic fields
Authors: Vaughan Theresa P.
Published: May 2009

LetKbe a field of characteristic different from 2, anda, bquadratically independent elements ofK.PutJ=K(√a, √b). In [4], Jensen and Yui discuss the question of quaternionic (Q8) extensions ofJ, and give a survey of known results. In [8], Ware discusses (among other things) some general conditions for, and relations between, the existence ofQ8andD4(dihedral) extensions ofK.A general theorem of Witt [9] says thatJwill have a quaternionic extensionJ(√u) if and only if there exists a 3 × 3 matrixPoverKsuch thatPPt= diag(a, b, 1/ab), and an appropriate value foruis given in terms of the entries ofP.The problem of actually findingPin a particular case is not trivial.
On a special class of finite 2-groups
Authors: Deaconescu Marian
Published: May 2009

In the course of classifying those finite groups F which have exactly five maximal subgroups, R. W. van der Waall [4] proved that one encounters the following situation. One class of such groups F is described by F = SP, where S = O2(F)∈Syl2(F), P ∈ Syl3(F), S/Φ(S) ≅ Z2 × Z2, P is cyclic and P operates via conjugation on 5 as a group of order 3, because in this case F/Φ(F) ≅ A4.
Extending Edgar's ordering to locally convex spaces
Authors: Robertson Neill
Published: May 2009

By the term “locally convex space”, we mean a locally convex Hausdorff topological vector space (see [17]). We shall denote the algebraic dual of a locally convex space E by E*, and its topological dual by E′. It is convenient to think of the elements of E as being linear functionals on E′, so that E can be identified with a subspace of E′*. The adjoint of a continuous linear map T:E→F will be denoted by T′:F′→E′. If 〈E, F〈 is a dual pair of vector spaces, then we shall denote the corresponding weak, strong and Mackey topologies on E by α(E, F), β(E, F) and μ(E, F) respectively.
Unbounded approximate identities in normed algebras
Authors: Dixon P. G.
Published: May 2009

The object of this paper is to consider two easy propositions concerning bounded approximate identities and show that they do not extend to unbounded approximate identities. The propositions are as follows.

Proposition 1.1. Every bounded left approximate identity in a normed algebra is a left approximate identity for the completion.

Proposition 1.2. Every bounded left approximate identity in a separable normed algebra has a subsequence which is a left approximate identity.
Normal closures of powers of Dehn twists in mapping class groups
Authors: Humphries Stephen P.
Published: May 2009

LetF = F(g, n)be an oriented surface of genusg≥1withn<2boundary components and letM(F)be its mapping class group. ThenM(F)is generated by Dehn twists about a finite number of non-bounding simple closed curves inF([6, 5]). See [1] for the definition of a Dehn twist. Letebe a non-bounding simple closed curve inFand letEdenote the isotopy class of the Dehn twist aboute. LetNbe the normal closure ofE2inM(F). In this paper we answer a question of Birman [1, Qu 28 page 219]:

Theorem 1.The subgroup N is of finite index in M(F).
Generalized injectivity and chain conditions
Authors: Dung Nguyen V.
Published: May 2009

Relationships between injectivity or generalized injectivity and chain conditions on a module category have been studied by several authors. A well-known theorem of Osofsky [14, 15] asserts that a ring all of whose cyclic right modules are injective is semisimple Artinian. Osofsky's proofs in [14, 15] essentially used homological properties of injective modules, and, later, her arguments were applied by other authors in their studies of rings for which cyclic right modules are quasi-injective, continuous or quasi-continuous (see e. g. [1, 10, 12]). Following [5] (cf. [4]), a module M is called a CS-module if every submodule of M is essential in a direct summand of M. In the recent paper [17], B. L. Osofsky and P. F. Smith have proved a very general theorem on cyclic completely CS-modules from which many known results in this area follow rather easily. In another direction, it was proved in [8] that a finitely generated quasi-injective module with ACC (respectively DCC) on essential submodules is Noetherian (respectively Artinian). This result was also extended to CS-modules in [3, 16], and weak CS-modules in [19].
Infinite dimensional representations of
Authors: Dean A. , Zorzitto F.
Published: May 2009

By a representation of the extended Dynkin diagram we shall mean a list of 5 vector spaces P, E1, E2, E3, E4 over an algebraically closed field K, and 4 linear maps a1, a2, a3, a4 as shown.

The spaces need not be of finite dimension.

In their solution of the 4-subspace problem [6], Gelfand and Ponomarev have classified such representations when the spaces are finite dimensional. A representation like (1) can also be viewed as a module over the K-algebra R4 consisting of all 5 × 5 matrices having zeros off the first row and off the main diagonal.
Serial rings with krull dimension
Authors: Chatters A. W.
Published: May 2009

A module is said to be serial if it has a unique chain of submodules, and a ring is serial if it is a direct sum of serial right ideals and a direct sum of serial left ideals. The serial rings of Krull dimension 0 are the Artinian serial (or generalised uniserial) rings studied by Nakayama and for which there is an extensive theory (see for example [4]). Warfield in [10] extended the theory to the non-Artinian case. In particular he showed that a Noetherian serial ring is a direct sum of Artinian serial rings and prime Noetherian serial rings, and he gave a structure theorem in the prime Noetherian case. A Noetherian non-Artinian serial ring has Krull dimension 1. Serial rings of arbitrary Krull dimension have been studied by Wright ([9], [12], [13], [14]) with special results being proved when the Krull dimension is 1 or 2.
Graphs with near v- and e-neighbourhoods
Authors: Fronček Dalibor
Published: May 2009

All the graphs considered in this paper are connected finite undirected graphs without loops and multiple edges.

By thevertex-neighbourhood (v-neighbourhood)of any vertexxin the graphGwe mean the subgraphinduced by the set of all vertices adjacent tox. Analogously by the edge-neighbourhood (e-neighbourhood) of any edgefwith end verticesx, ywe mean the subgraph(f) (or(xy)) induced by the set of all vertices which are adjacent to at least one vertex of the pair x, y and which are different fromx, y.
The normalizer of Γ0(N) in PSL(2, ℝ)
Authors: Akbas M. , Singerman D.
Published: May 2009

Let Γ denote the modular group, consisting of the Möbius transformations

As usual we denote the above transformation by the matrix remembering that V and – V represent the same transformation. If N is a positive integer we let Γ0(N) denote the transformations for which c ≡ 0 mod N. Then Γ0(N) is a subgroup of index

the product being taken over all prime divisors of N.
Principally ordered regular semigroups
Authors: Blyth T. S. , Pinto G. A.
Published: May 2009

An ordered semigroup S will be called principally ordered if, for every x ɛ S, there exists

x* = max {y ɛ S; xyx ≤ x}.

Here we shall be concerned with the case where S is regular. We begin by listing some basic properties that arise from the above definition. As usual, we shall denote by V(x) the set of inverses of x ɛ S.
Pairs of quadratic forms modulo one
Authors: Baker R. C. , Brüdern J.
Published: May 2009

Let s be a natural number, s ≥ 2. We seek a positive number λ(s) with the following property:

Let ε > 0. Let Q1(x1, …, xs), Q2(x1, …, xs) be real quadratic forms, then for N > C1(s, ε) we have

for some integers n1, …, ns,
Cohomological periodicity in graph products of combinatorially aspherical groups
Authors: Horadam K. J.
Published: May 2009

The notion of a group G having periodic cohomology after k steps was introduced by Talelli in [10], and is equivalent to having the functors Hm(G, —) and Hm+q(G, —) naturally isomorphic for some q ≥ 1 and all m ≥k + 1. It extends to infinite groups the long-understood phenomenon of cohomological periodicity for finite groups (for which k = 0).
Isoparametric functions and submanifolds
Authors: Kashani S. M. B.
Published: May 2009

The theory of isoparametric functions and a family of isoparametric hypersurfaces began essentially with E. Cartan in 1930's. He defined a real valued function V defined on a Riemannian space form to be isoparametric if ∥grad υ∥2=TV and ΔV = SV for some real valued functions S, T. Then a family of hypersurfaces Mt, is called isoparametric if Mt,=V-1 (t) where t is a regular value of V.
Covering a group with isolators of finitely many subgroups
Authors: Longobardi Patrizia , Maj Mercede , Rhemtulla Akbar H.
Published: May 2009

In [6] B. H. Neumann proved the following beautiful result:if a group G is covered by finitely many cosets, say G=xiHi, then we can omit from the union any xiHi, for which|G|Hj|is infinite. In particular, |G:Hj|is finite, for some j∈ {l,…,n}.

In an unpublished result R. Baer characterized the groups covered by finitely many abelian subgroups, they are exactly the centre-by-finite groups [8]. Coverings by nilpotent subgroups or by Engel subgroups and by normal subgroups have been studied, for example, by R. Baer (see [8]), L. C. Kappe [2,1], M. A. Brodie and R. F. Chamberlain [1], and recently by M. J. Tomkinson [9].
On congruences of double p-algebras with nonvoid core
Authors: Koubek V. , Sichler J.
Published: May 2009

An algebra L = L = (A; V, Λ, *, +, 0, 1) of type (2, 2, 1, 1, 0, 0) is called a distributive double p-algebra whenever its reduct (A, V, Λ, 0, 1) is a distributive (0, 1)-lattice that, for any a ∈ A, contains a greatest element a* such that a Λ a* = 0 and a least element a+ for which a v a+ = 1.
Some properties of orthogonal polynomials satisfying fourth order differential equations
Authors: Campos R. G. , Avila L. A.
Published: May 2009

In the last few years, there has been considerable interest in the properties of orthogonal polynomials satisfying differential equations (DE) of order greater than two, their connection to singular boundary value problems, their generalizations, and their classification as solutions of second order DE (see for instance [2–8]). In this last interesting problem, some known facts about the classical orthogonal polynomials can be incorporated to connect these two sets of families and yield some nontrivial results in a very simple way. In this paper we only work with the nonclassical Jacobi type, Laguerre type and Legendre type polynomials, and we show how they can be connected with the classical Jacobi, Laguerre and Legendre polynomials, respectively; at the same time we obtain certain bounds for the zeros of the first ones by using a system of nonlinear equations satisfied by the zeros of any polynomial solution of a second order differential equation which, for the classical polynomials is known since Stieltjes and concerns the electrostatic interpretation of the zeros [10, Section 6.7; 9,1]. We also correct an expression for the second order differential equation of the Legendre type polynomials that circulates through the literature.
The Chen-type of the noncompact cyclides of Dupin
Authors: Defever Filip , Deszcz Ryszard , Verstraelen Leopold
Published: May 2009

Minimal submanifolds of a Euclidean space are contained in a much larger class of submanifolds, namely in the class of submanifolds of finite type. Submanifolds of finite type were introduced about a decade ago by B. Y. Chen in [2]; the first results on this subject have been collected in the books [2], [3].
Spectral properties of p-hyponormal operators
Authors: Chō Muneo
Published: May 2009

Let ℋ be a complex Hilbert space and B(ℋ) be the algebra of all bounded linear opeators on ℋ. An operator T ∈ B(ℋ) is said to be p-hyponormal if (T*T)p–(TT*)p. If p = 1, T is hyponormal and if p = ½ is semi-hyponormal. It is well known that a p-hyponormal operator is p-hyponormal for q≤p. Hyponormal operators have been studied by many authors. The semi-hyponormal operator was first introduced by D. Xia in [7]. The p-hyponormal operators have been studied by A. Aluthge in [1]. Let T be a p-hyponormal operator and T=U|T| be a polar decomposition of T. If U is unitary, Aluthge in [1] proved the following properties.
Almost-Dedekind rings
Authors: Johnson E. W.
Published: May 2009

Throughout we assume all rings are commutative with identity. We denote the lattice of ideals of a ringRbyL(R), and we denote byL(R)* the subposetL(R)−R.

A classical result of commutative ring theory is the characterization of a Dedekind domain as an integral domainRin which every element ofL(R)* is a product of prime ideals (see Mori [5] for a history). This result has been generalized in a number of ways. In particular, rings which are not necessarily domains but which otherwise satisfy the hypotheses (i.e. general ZPI-rings) have been widely studied (see, for example, Gilmer [3]), as have rings in which only the principal ideals are assumed to satisfy the hypothesis (i.e. π-rings).
Linearization of holomorphic mappings on fully nuclear spaces with a basis
Authors: Dineen Seán , Galindo Pablo , García Domingo , Maestre Manuel
Published: May 2009

In [13] Mazet proved the following result.

If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;

The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].
The structure of discontinuous homomorphisms from non-commutative C*-algebras
Authors: Runde Volker
Published: May 2009

LetXbe a compact Hausdorff space, letC(X)denote the algebra of all continuous functions onX, letBbe a Banach algebra, and let θ: →C(X)→Bbe a (possibly discontinuous) homomorphism with dense range. A classical theorem by W. G. Bade and P. C. Curtis ([2, Theorem 4.3]) describes in great detail the structure of θ we shall refer to this result as the Bade–Curtis theorem. Before we give a brief sketch of this theorem, we fix some notation. ForY⊂XletI(Y)andJ(Y)denote the ideals of all functions inC(X)that vanish onYand on a neighborhood ofYrespectively; ifY= {x} for somexɛX, we write mxandJxforI(Y)andJ(Y)respectively. According to the Bade–Curtis theorem there is a finite set {x1,…, xn) ⊂X, the so-calledsingularity setof θ, such that θ | ({x1, …, xn}) is continuous. As a consequence, the restriction of θ to the dense subalgebra ofC (X)consisting of all those functions which are constant near eachXj(j= 1,…,n) is continuous, and extends to a continuous homomorphism θcont:C(X)→B. Let θsing: = θ – θcont. Then θsing|I({x1,…, xn}) is a homomorphism onto a dense subalgebra of rad (B). θcont, and θsingare called thecontinuousand thesingular partof θ respectively. Moreover, there are linear maps:C(X)⊒Bsuch that

(i)

(ii)is a homomorphism, and

Condition (iii) forces the homomorphismsto map into rad(B); such homomorphisms are calledradical homomorphisms.
On the Arens semi-regularity of weighted group algebras
Authors: Argün Ziya , Rowlands K.
Published: May 2009

In this paper we prove that the weighted group algebra L1 (G, w) is semi-regular if and only if G is either abelian or discrete.
On the Diophantine equation z2 = x4 + Dx2y2 + y4
Authors: Cohn J. H. E.
Published: May 2009

The equation of the title in positive integers x, y, z where D is a given integer has been considered for some 300 years [4, pp 634–639]. As observed by V. A. Lebesgue, and probably known to Euler, if x, y, z is one non-trivial solution i.e., one with xy(x2 – y2) ≠0, another is given by . It then follows that there are infinitely many such with (x, y) = 1. The question that remains is to determine for which values of D such solutions exist.
On stationary phase integrals
Authors: Huxley M. N.
Published: May 2009

Let f(x) and g(x) be real functions defined on the interval [a, b], with f(x) at least twice continuously differentiable, f′(x) monotone increasing, and f(x) of bounded variation. We consider the exponential integral

where e(t) denotes exp 2πit. The purpose of this note is to prove sharp forms of the well-known estimates:

A: If f′(x) is nonzero on [a, b], then I has order of magnitude

The constant of proportionality depends on the function g(x).

B: If f′(x) changes sign at x = c with a < c < b, then
Singular pleated surfaces and CP1–structures
Authors: Tan Ser Peow
Published: May 2009

Let Fg be a closed orientable surface of genus g > 1 and let be the Teichmuller space of Fg, i.e., the space of marked hyperbolic structures on Fg We shall also denote by the space of marked hyperbolic structures on Fgwith one distinguished point; by this, we mean a distinguished point on the universal cover gof Fg. This space is isomorphic to the space of marked complete hyperbolic structures on a genus g surface with 1 cusp which is the usual interpretation of . Choose a decomposition of Fginto pairs of pants by a collection of non–intersecting, totally geodesic simple closed curves. The Fenchel–Nielsen coordinates for relative to this decomposition are given by the lengths of the curves as well as twist parameters defined on each curve. Varying the length and twist parameters gives deformations of the marked hyperbolic structures.
Skew group rings and maximal orders
Authors: Martin R.
Published: May 2009

Let S be a prime Noetherian ring and G a finite group acting on 5 such that Gis x-outer on S. We give sufficient conditions for the skew group ring S * Gto be a prime maximal order. If we impose the further hypothesis that the order of Gbe a unit of S, then these conditions are also necessary. Moreover, if S is a commutative Noetherian domain, then there are necessary and sufficient conditions for S*Gto be a prime maximal order, without requiring that the order of G be a unit in S.
Perfect Pell Powers
Authors: Cohn J. H. E.
Published: May 2009

In the thirty years since it was proved that 0, 1 and 144 were the only perfect squares in the Fibonacci sequence [1, 9], several generalisations have been proved, but many problems remain. Thus it has been shown that 0, 1 and 8 are the only Fibonacci cubes [6] but there seems to be no method available to prove the conjecture that 0, 1, 8 and 144 are the only perfect powers.
A simple proof of Noether's theorem
Authors: Chapman Robin J.
Published: May 2009

We present an elementary proof of the theorem, usually attributed to Noether, that ifL/Kis a tame finite Galois extension of local fields, thenis a free-module where Γ=Gal(L/K. The attribution to Noether is slightly misleading as she only states and proves the result in the case where the residual characteristic ofKdoes not divide the order of Γ [4]. In this caseis a maximal order inKΓ which is not true for general groups Γ. There is an elegant proof in the standard reference [2], but this relies on a difficult result in representation theory due to Swan. Our proof depends on a close examination of the structure of tame local extensions, and uses only elementary facts about local fields. It also gives an explicit construction of a generator element, and the same proof works both for localizations of number fields and of global function fields.
Nontrivial solutions for a multivalued problem with strong resonance
Authors: Rădulescu Vicenţiu D.
Published: May 2009

The Mountain-Pass Theorem of Ambrosetti and Rabinowitz (see [1]) and the Saddle Point Theorem of Rabinowitz (see [21]) are very important tools in the critical point theory of C1-functional. That is why it is natural to ask us what happens if the functional fails to be differentiable. The first who considered such a case were Aubin and Clarke (see [6]) and Chang (see [12]),who gave suitable variants of the Mountain-Pass Theorem for locally Lipschitz functionals which are denned on reflexive Banach spaces. For this aim they replaced the usual gradient with a generalized one, which was firstly defined by Clarke (see [13], [14]).As observed by Brezis (see [12, p. 114]), these abstract critical point theorems remain valid in non-reflexive Banach spaces.
Finite co-Dedekindian groups
Authors: Deaconescu Marian , Silberberg Gheorghe
Published: May 2009

A group G is called Dedekindian if every subgroup ofG is normal in G.

The structure of the finite Dedekindian groups is well-known [3, Satz 7.12]. They are either abelian or direct products of the form Q × A × B, where Q is the quaternion group of order 8, Ais abelian of odd order and exp(B) ≤ 2.
Boundaries of nonpositively curved groups of the form G × ℤn
Authors: Bowers Philip L. , Ruane Kim
Published: May 2009

The introduction of curvature considerations in the past decade into Combinatorial Group Theory has had a profound effect on the study of infinite discrete groups. In particular, the theory of negatively curved groups has enjoyed significant and extensive development since Cannon's seminal study of cocompact hyperbolic groups in the early eighties [7]. Unarguably the greatest influence on the direction of this development has been Gromov's tour de force, his foundational essay in [12] entitled Hyperbolic Groups. Therein Gromov hints at the prospect of developing a corresponding theory of “non-positively curved groups” in his non-definition (Gromov's terminology) of a semihyperbolic group as a group that “looks as if it admits a discrete co-compact isometric action on a space of nonpositive curvature”; [12, p. 81]. Such a development is now occurring and is closely related to the other notable outgrowth of the theory of negatively curved groups, that of automatic groups [10]; we mention here the works [3] and [6] as developments of a theory of nonpositively curved groups along with Chapter 6 of Gromov's more recent treatise [13]. A natural question that serves both to guide and organize the developing theory is: to what extent is the well-developed theory of negatively curved groups reflected in and subsumed under the developing theory of nonpositively curved groups? Our overall interest is in one aspect of this question—namely, as the question relates to the boundaries of groups and spaces: can one define the boundary of a nonpositively curved group intrinsically in a way that generalizes that of negatively curved groups and retains some of their essential features?
Strong bands of groups of left quotients
Authors: Ćirić Miroslav , Bogdanović Stojan
Published: May 2009

An interesting concept of semigroups (and also rings) of (left) quotients, based on the notion of group inverse in a semigroup, was developed by J. B. Fountain, V. Gould and M. Petrich, in a series of papers (see [5]-[12]). Among the most interesting are semigroups having a semigroup of (left) quotients that is a union of groups. Such semigroups have been widely studied. Recall from [3] that a semigroup has a group of left quotients if and only if it is right reversible and cancellative. A more general result was obtained by V. Gould [10]. She proved that a semigroup has a semilattice of groups as its semigroup of left quotients if and only if it is a semilattice of right reversible, cancellative semigroups. This result has been since generalized by A. El-Qallali [4]. He proved that a semigroup has a left regular band of groups as its semigroup of left quotients if and only if it is a left regular band of right reversible, cancellative semigroups. Moreover, he proved that such semigroups can be also characterised as punched spined products of a left regular band and a semilattice of right reversible, cancellative semigroups. If we consider the proofs of their theorems, we will observe that the principal problem treated there can be formulated in the following way: Given a semigroup S that is a band B of right reversible, cancellative semigroups Si, i ε B, to each Si, we can associate its group of left quotients Gi. When is it possible to define a multiplication of such that Q becomes a semigroup having S as its left order, and especially, that Q becomes a band B of groups Gi, i E B?Applying the methods developed in [1] (see also [2]), in the present paper we show how this problem can be solved for Qto become a strong band of groups (that is in fact a band of groups whose idempotents form a subsemigroup, by [16, Theorem 2]. Moreover, we show how Gould's and El-Quallali's constructions of semigroups of left quotients of a semilattice and a left regular band of right reversible, cancellative semigroups, can be simplified.
Prime and maximal ideals in polynomial rings
Authors: Ferrero Miguel
Published: May 2009

In this paper we study prime and maximal ideals in a polynomial ring R[X], where R is a ring with identity element. It is well-known that to study many questions we may assume Ris prime and consider just R-disjoint ideals. We give a characterizaton for an R-disjoint ideal to be prime. We study conditions under which there exists an R-disjoint ideal which is a maximal ideal and when this is the case how to determine all such maximal ideals. Finally, we prove a theorem giving several equivalent conditions for a maximal ideal to be generated by polynomials of minimal degree.
Finite groups generated by subnormalT-subgroups
Authors: Cossey John
Published: May 2009

Our aim in this paper is to investigate the restrictions placed on the structure of a finite group if it can be generated by subnormalT-subgroups (aT-group is a group in which every subnormal subgroup is normal). For notational convenience we denote bythe class of finite groups that can be generated by subnormalT-subgroups and bythe subclass ofof those finite groups generated by normalT-subgroups; and for the remainder of this paper we will only consider finite groups.
Grothendieck's property in Lp(μ, X)
Authors: Díaz Santiago
Published: May 2009

We prove that, for non purely atomic measures, Lp (μ, X) is a Grothendieck space if and only if X is reflexive.
A generalized Drazin inverse
Authors: Koliha J. J.
Published: May 2009

The main theme of this paper can be described as a study of the Drazin inverse for bounded linear operators in a Banach spaceXwhen 0 is an isolated spectral point ofthe operator. This inverse is useful for instance in the solution of differential equations formulated in a Banach spaceX. Since the elements ofXrarely enter into our considerations, the exposition seems to gain in clarity when the operators are regarded as elements of the Banach algebraL(X).
The minimal degree of a faithful quasi-permutation representation of an abelian group
Authors: Behravesh Houshang
Published: May 2009

Let G be a finite linear group of degree n; that is, a finite group of automorphisms of an n-dimensional complex vector space (or, equivalently, a finite group of non-singular matrices of order n with complex coefficients). We shall say that G is a quasi-permutation group if the trace of every element of G is a non-negative rational integer. The reason for this terminology is that, if G is a permutation group of degree n, its elements, considered as acting on the elements of a basis of an n -dimensional complex vector space V, induce automorphisms of V forming a group isomorphic to G. The trace of the automorphism corresponding to an element x of G is equal to the number of letters left fixed by x, and so is a non-negative integer. Thus, a permutation group of degree n has a representation as a quasi-permutation group of degree n. See [5].
The KO-cohomology ring of SU (2n)/SO (2 n)
Authors: Watanabe Takashi
Published: May 2009

The KO-cohomology ring of the symmetric space SU(2n)/SO(2n) is computed by using the Bott exact sequence and some facts on the real and quaternionic representation rings of SU(2n) and SO(2n).
On product k-Chen submanifolds
Authors: Dursunf Uǧur
Published: May 2009

B. Rouxel [7] and S. J. Li and C. S. Houh [6] have generalised the notion of an -submanifold (Chen submanifold) to an k-submanifold. In [1] we have studied the relation between their definitions for the Euclidean case.
A note on the punctured neighbourhood theorem
Authors: Harte Robin , Leef Woo Young
Published: May 2009

The punctured neighbourhood theorem an be interpreted as saying that if 0 ∈ C is on the boundary of the spectrum of a Fredholm operator then it must be an isolated point of that spectrum. This extends to semi-Fredholm operators, in particular to operators with closed range and finite dimensional null space. In this note we generalise both the finite dimensionality of the null space and the scalars involved in the definition of an isolated point of the spectrum.
Automatic continuity of certain isomorphisms between regular Banach function algebras
Authors: Font Juan J.
Published: May 2009

LetAandBbe regular semisimple commutative Banach algebras; that is to say, regular Banach function algebras. A linear mapTdenned fromAintoBis said to beseparatingordisjointness preservingiff.g = 0 impliesTf.Tg= 0, for allf, g∈ A In this paper we prove that ifAsatisfies Ditkin's condition then a separating bijection isautomatically continuousand its inverse is separating. If alsoBsatisfies Ditkin's condition, then it induces a homeomorphism between the structure spaces ofAandB.
Totally real pseudo-umbilical submanifolds of a quaternion space form
Authors: Sun Huafei
Published: May 2009

Let M(c) denote a 4n-dimensional quaternion space form of quaternion sectional curvature c, and let P(H) denote the 4n-dimensional quaternion projective space of constant quaternion sectional curvature 4. Let N be an n-dimensional Riemannian manifold isometrically immersed in M(c). We call N a totally real submanifold of M(c) if each tangent 2-plane of N is mapped into a totally real plane in M (c). B. Y. Chen and C. S. Houh proved in [1].
Annihilators and the CS-condition
Authors: Nicholson W. K. , Yousif M. F.
Published: May 2009

It is proved that if every cyclic right R-module is torsionless and R is a left CS-ring then R is semiperfect left continuous with soc(RR)essential in RR. As a consequence every right cogenerator, left CS-ring R is shown to be right pseudo-Frobenius and left continuous, and an example is given to show that R need not be left selfinjective. It is also proved that if R is a left CS-ring and every cyclic right R-module embeds in a free module, then R is quasi-Frobenius if and only if J(R) ⊆ Z(RR).