bluuebunny/crossref_metadata_2025 huggingface dataset:
On non-zero values of the central homological dimension of C*-algebras
Authors: Lykova Z. A.
Published: May 2009

The paper is related to the area which was recently called topological homology [3, 6, 12, 16, 4]. We consider questions associated with the central Hochschild cohomology of C*-algebras. The study of the latter was begun by J. Phillips and I. Raeburn in [9, 10], when they were investigating some problems of the theory of perturbations of C*-algebras. In [8] we obtained a description of the structure of C*-algebras with central bidimension zero: it was proved that these C*-algebras are unital and have continuous trace. In the special case of separable and a priori unital C*-algebras this statement was proved by J. Phillips and I. Raeburn in [11] with the help of a different approach. The question was raised. Which values can the central bidimension of C*-algebras take? In the present paper it is shown that, for any CCR-algebra A having at least one infinite-dimensional irreducible representation, the central bidimension and the global central homological dimension of A are greater than one. At the same time it is proved that there exist CCR-algebras which are centrally biprojective, but which have both dimensions equal to one. This situation contrasts with the state of affairs in the “traditional” theory of the Banach Hochschild cohomology. Recall [3, Ch. 5] that the bidimension and the global homological dimension of any infinite-dimensional biprojective C*-algebra are equal to two. Besides, there is no CCR-algebra of bidimension one (respectively, global homological dimension one). See [7].
Moduli of endomorphisms of semistable vector bundles over a compact Riemann surface
Authors: Paz L. Brambila
Published: May 2009

Mumford and Suominen in [8] and Newstead in [11] have considered the moduli problem of classifying the endomorphisms of finite-dimensional vector spaces. Using similar ideas we consider the moduli problem for endomorphisms of indecomposable semistable vector bundles over a compact connected Riemann surface of genus g ≥ 2.
On (V*) sets and Pelczynski's property (V*)
Authors: Bombal Fernando
Published: May 2009

The concept of (V*) set was introduced, as a dual companion of that of (V)-set, by Pelczynski in his important paper [14]. In the same paper, the so called properties (V) and (V*) are defined by the coincidence of the (V) or (V*) sets with the weakly relatively compact sets. Many important Banach space properties are (or can be) defined in the same way; that is, by the coincidence of two classes of bounded sets. In this paper, we are concerned with the study of the class of (V*) sets in a Banach space, and its relationship with other related classes. To this general study is devoted Section I. A (as far as we know) new Banach space property (we called it property weak (V*)) is defined, by imposing the coincidence of (V*) sets and weakly conditionally compact sets. In this way, property (V*) is decomposed into the conjunction of the weak (V*) property and the weak sequential completeness. In Section II, we specialize to the study of (V*) sets in Banach lattices. The main result in the section is that every order continuous Banach lattice has property weak (V*), which extends previous results of E. and P. Saab ([16]). Finally, Section III is devoted to the study of (V*) sets in spaces of Bochner integrable functions. We characterize a broad class of (V*) sets in L1(μ, E), obtaining similar results to those of Andrews [1], Bourgain [6] and Diestel [7] for other classes of subsets. Applications to the study of properties (V*) and weak (V*) are obtained. Extension of these results to vector valued Orlicz function spaces are also given.
On right duo p.p. rings
Authors: Chatters A. W. , Xue Weimin
Published: May 2009

Throughout the paper, rings are associative rings with identity. A ring is called right duo if every right ideal is two-sided, and it is called right p.p. if every principal right ideal is projective. A left duo (p.p.) ring is denned similarly, and a duo (p.p.) ring will mean a ring which is both right and left duo (p.p.). There is a right p.p. ring that is not left p.p. (see Chase [2[). Small [9] proved that right p.p. implies left p.p. if there are no infinite sets of orthogonal idempotents, and Endo [5, Proposition 2] has shown the same implication in the case where each idempotent in the ring is central. Since Courter [3, Theorem 1.3] noted that every idempotent in a right duo ring is central, we can simply speak of right duo p.p. rings. A typical example of a right duo ring which is not left duo is the following. Let F be a field and F(x) the field of rational functions over F. Let R = F(x)× F(x) as an additive group and define the multiplication as follows:

Then R is a local artinian ring with c(RR) = 2 and c(RR)= 3. Thus R is right duo but not left due.
Matrix invariants and complete intersections
Authors: le Bruyn Lieven , Teranishi Yasuo
Published: May 2009

Consider the vector space of m-tuples of n by n matrices

.

The linear group GLn(C) acts on Xm, n by simultaneous conjugation. The corresponding ring of polynomial invariants

will be denoted by C(n, m) and is called the ring of matrix invariants of m-tuples of n by n matrices. C. Procesi has shown in [8] that C(n, m) is generated by traces of products of the corresponding generic matrices and, as such, coincides with the center of the trace ring of m generic n by n matrices R (n, m) which is also the ring of equivariant maps from Xm, n to Mn(ℂ).
Corrigendum
Authors: Campbell James T. , Jamison James E.
Published: May 2009

We provide corrected versions of Theorems 1 and 2 and Corollaries 3(a) and 4 of the paper mentioned in the title.
Deciding if an automorphism of an infinite soluble group is inner
Authors: Robinson Derek J. S.
Published: May 2009

Let G be a group with a finite set of generators x1, x2,…,xn and a recursive set of defining relators in the generators. Then an endomorphism η of G is completely determined by the images of the generators , and hence by the n-tuple of words in x, (w1,…,wn). This allows the formulation of algorithmic problems about endomorphisms and automorphisms. For example, can one decide if a given n-tuple of words represents an endomorphism, and if so, an automorphism? Some results on these questions may be found in [2] and [12]. Here we shall be concerned with a similar problem: given that an n-tuple of words represents an automorphism of the group G, does there exist an algorithm which decides if the automorphism is inner?
The λ-property in schreier's space S and the Lorentz space d(a, 1)
Authors: Shura Thaddeus J. , Trautman David
Published: May 2009

We add Schreier's space S and the Lorentz space d(a, 1) to the list of classical Banach spaces which enjoy the λ-property, investigate the extreme point structure of S, and show that d(a, 1) has a λ-function which is continuous on Sd(a, 1), though not even uniformly so.
A coordinate-free approach to surface kinematics
Authors: Murdoch A. I.
Published: May 2009

A thin three-dimensional material system, such as a thin shell or fluid-fluid interface, is often modelled as a bidimensional continuous body which at any instant “occupies” some geometrical surface. The time evolution of such surfaces is usually described in terms of curvilinear coordinates [2], [4], [6], a procedure which can mask the geometry involved. An alternative, coordinate-free, approach has been employed [1], [3] which patently exhibits the fundamental geometric (and algebraic) aspects of the kinematics of deforming surfaces. The foundations of this approach are presented in Section 2, following introductory remarks on notation and calculus in Euclidean point spaces, and hitherto unpublished results are developed in Section 3. Account is taken both of material and non-material surfaces: in the former case (surface) mass is conserved (this will be true for thin solid shells) while in the latter context mass exchange with contiguous phases is possible (as is to be expected in the case of fluid-fluid interfaces). The results are also pertinent to singular surfaces [2], [6], [7] (such as shock waves) which are not endowed with intrinsic material attributes but rather with discontinuities of bulk quantities.
On the symmetric algebra of quotients of a C*-algebra
Authors: Ara Pere
Published: May 2009

Let R be a semiprime ring (possibly without 1). The symmetric ring of quotients of R is defined as the set of equivalence classes of essentially defined double centralizers (ƒ, g) on R; see [1], [8]. So, by definition, ƒ is a left R-module homomorphism from an essential ideal I of R into R, g is a right R-module homomorphism from an essential ideal J of R into R, and they satisfy the balanced condition ƒ(x)y = xg(y) for x ∈ Iand y ∈ J. This ring was used by Kharchenko in his investigations on the Galois theory of semiprime rings [4] and it is also a useful tool for the study of crossed products of prime rings [7]. We denote the symmetric ring of quotients of a semiprime ring R by Q(R).
A note on GV-modules with Krull dimension
Authors: Huynh van Dinh , Smith Patrick F. , Wisbauer Robert
Published: May 2009

Extending a result of Boyle and Goodearl in [1] on V-rings it was shown in Yousif [11] that a generalized V-module (GV-module) has Krull dimension if and only if it is noetherian. Our note is based on the observation that every GV-module has a maximal submodule (Lemma 1). Applying a theorem of Shock [6] we immediately obtain that a GV-module has acc on essential submodules if and only if for every essential submodule K ⊂ M the factor module M/K has finitely generated socle. Yousif's result is obtained as a corollary.

Let R be an associative ring with unity and R-Mod the category of unital left R-modules. Soc M denotes the socle of an R-module M. If K ⊂ M is an essential submodule we write K⊴M.

An R-module M is called co-semisimple or a V-module, if every simple module is M-injective ([2], [7], [9], [10]). According to Hirano [3] M is a generalized V-module or GV-module, if every singular simple R-module is M-injective. This extends the notion of a left GV-ring in Ramamurthi-Rangaswamy [5].

It is easy to see that submodules, factor modules and direct sums of co-semisimple modules (GV-modules) are again co-semisimple (GV-modules) (e.g. [10, § 23]).
Normal-convex embeddings of inverse semigroups
Authors: Silva Pedro V.
Published: May 2009

Normal-convex embeddings are introduced for inverse semigroups, generalizing the group-theoretic concept, due to Papakyriakopoulos [4]. It is shown that every E-unitary inverse semigroup admits a normal-convex embedding into a semidirect product of a semilattice by a group, a stronger version of a result by O'Carroll [3]. A general embedding result for inverse semigroups is also obtained.
Components in vector lattices and extreme extensions of quasi-measures and measures
Authors: Lipecki Z.
Published: May 2009

We develop some ideas contained in the author's paper [8] which was, in turn, inspired by Bierlein and Stich [5]. The main body of the present paper is divided into three sections. Section 2 is concerned with some vector-lattice-theoretical results. They are then applied to extensions of quasi-measures and measures in Sections 3 and 4, respectively.

Let X be a vector lattice, let x ε X+ and let S be a non-empty set. Theorems 1 and 2 describe some properties of the convex set

(see Section 2 for the definition of the sum above). The extreme points of Dx,s are characterized in terms of the components of x. It is also shown that if X has the principal projection property and S is countable, then extr Dx,s is, in some sense, large in Dx,s. Furthermore, for finite S, each point in Dx,s is then a sσ-convex combination of extreme ones.
An infinitesimal proof of the implicit function theorem
Authors: Cutland Nigel J. , Hanqiao Feng
Published: May 2009

We give a short and constructive proof of the general (multi-dimensional) Implicit Function Theorem (IFT), using infinitesimal (i.e. nonstandard) methods to implement our basic intuition about the result. Here is the statement of the IFT, quoted from [4];

Theorem. Let A ⊂ ℝn × ℝmbe an open set and let F:A → ℝ be a function of class Cp (p≥1). Suppose that (xO, yO) ε A with F(xO, yO) = 0 (xO ε ℝn, yO ε ℝm) and that the Jacobian determinantis not zero at (xO, yO). Then there is an open neighbourhood U of xO and a unique function f:U→ ℝmwith

F(x, f(x)) = 0

for all x ε U. Moreover, f is of class Cp.
Finite coverings by subgroups with a given property
Authors: Brodie Marc A. , Kappe Luise-Charlotte
Published: May 2009

Letbe a group-theoretic property. We say a group has a finite covering by-subgroups if it is the set-theoretic union of finitely many-subgroups. The topic of this paper is the investigation of groups having a finite covering by nilpotent subgroups,n-abelian subgroups or 2-central subgroups.

R. Baer [12; 4.16] characterized central-by-finite groups as those groups having a finite covering by abelian subgroups. In [6] it was shown that [G: ZC(G)] finite implies the existence of a finite covering by subgroups of nilpotency classc, i.e. ℜc-groups. However, an example of a group is given there which has a finite covering by ℜ2-groups, butZ2(G) does not have finite index in the group. These results raise two questions, on which we will focus our investigations.
The Diophantine equation x2+3 = yn
Authors: Cohn J. H. E.
Published: May 2009

Many special cases of the equation x2+C= yn where x and y are positive integers and n≥3 have been considered over the years, but most results for general n are of fairly recent origin. The earliest reference seems to be an assertion by Fermat that he had shown that when C=2, n=3, the only solutions are given by x = 5, y = 3; a proof was published by Euler [1]. The first result for general n is due to Lebesgue [2] who proved that when C = 1 there are no solutions. Nagell [4] generalised Fermat's result and proved that for C = 2 the equation has no solution other than x = 5, y = 3, n = 3. He also showed [5] that for C = 4 the equation has no solution except x = 2, y = 2, n = 3 and x = 11, y = 5, n = 3, and claims in [6] to have dealt with the case C = 5. The case C = -1 was solved by Chao Ko, and an account appears in [3], pp. 302–304.
Banach spaces with property (w)
Authors: Leung Denny H.
Published: May 2009

A Banach spaceEis said to haveProperty(w) if every operator fromEintoE' is weakly compact. This property was introduced by E. and P. Saab in [9]. They observe that for Banach lattices, Property (w) is equivalent to Property (V*), which in turn is equivalent to the Banach lattice having a weakly sequentially complete dual. Thus the following question was raised in [9].

Does every Banach space with Property (w) have a weakly sequentially complete dual, or even Property (V*)?

In this paper, we give two examples, both of which answer the question in the negative. Both examples are James type spaces considered in [1]. They both possess properties stronger than Property (w). The first example has the property that every operator from the space into the dual is compact. In the second example, both the space and its dual have Property (w). In the last section we establish some partial results concerning the problem (also raised in [9]) of whether (w) passes from a Banach spaceEtoC(K, E).
A note on reductions of ideals relative to an Artinian module
Authors: Taherizadeh A.-J.
Published: May 2009

The concept of reduction and integral closure of ideals relative to Artinian modules were introduced in [7]; and we summarize some of the main aspects now.

Let A be a commutative ring (with non-zero identity) and let a, b be ideals of A. Suppose that M is an Artinian module over A. We say that a is a reduction of b relative to M if a ⊆ b and there is a positive integer s such that

)O:Mabs)=(O:Mbs+l).

An element x of A is said to be integrally dependent on a relative to M if there exists n y ℕ(where ℕ denotes the set of positive integers) such that

It is shown that this is the case if and only if a is a reduction of a+Ax relative to M; moreover

ᾱ={x ɛ A: xis integrally dependent on a relative to M}

is an ideal of A called the integral closure of a relative to M and is the unique maximal member of

℘ = {b: b is an ideal of A which has a as a reduction relative to M}.
Countable enlargements of norm topologies and the quasidistinguished property
Authors: Catalan F. X. , Tweddle I.
Published: May 2009

Let E be a Hausdorff locally convex space with continuous dual E1 and let M be a subspace of the algebraic dual E* such that M ∩ E1 = {0} and dim M = ℵ0. In the terminology of [4] the Mackey topology τ(E, E1 + M) is called a countable enlargement of τ(E, E1). There has been some interest in the question of when barrelledness is preserved under countable enlargements (see [4], [5], [6], [8], [9]). In this note we are concerned with the preservation of the quasidistinguished property for normed spaces under countable enlargements; this was posed as on open question by B. Tsirulnikov in [7]. According to [7] a Hausdorff locally convex space E is quasidistinguished if every bounded subset of its completion Ê is contained in the completion of a bounded subset of Ê (equivalently, in the closure in Ê of a bounded subset of E). Any normed space is clearly quasidistinguished and remains so under a finite enlargement (dim M < χ0) since the enlarged topology is normable. (See the Main Theorem of [7] for a general result on the preservation of the quasidistinguished property under finite enlargements.) We shall write QDCE for a countable enlargement which preserves the quasidistinguished property.
Representation of primes by binary quadratic forms of discriminant –256q and –128q
Authors: Halter-Koch Franz
Published: May 2009

Recently, P. Kaplan and K. S. Williams [10] considered (as an example) the representation of primes by binary quadratic forms of discriminant –768. These forms fall into 4 genera, each consisting of two classes. In particular, they considered the forms

F=3X2+642 and G = 12X2+12XY+19Y2.

It follows from genus theory (as explained in [10]) that every prime p ≡ 19 mod 24 is represented by exactly one of the forms F and G. Based on numerical data, they conjectured that a prime p ≡ 19 mod 24 is represented by

where

Vo = 2, V1 = -4, Vn+2=-4Vn+1 -Vn (n∨0).
Metacyclic p-groups and their conjugacy classes of subgroups
Authors: Brandl Rolf , Verardi Libero
Published: May 2009

Let G be a group and let ℓ(G) be the set of all conjugacy classes [H] of subgroups H of G, where a partial order ≤ is defined by [H1] ≤ [H2] if and only if H1, is contained in some conjugate of H2.

A number of papers (see for example [1] and the references mentioned there) deal with the question of characterizing groups G by the poset ℓ(G). For example, in [1] it was shown that if ℓ(G) and ℓ(H) are order-isomorphic and G is a noncyclic p-group then |G| = |H|. Moreover, if G is abelian, then G = H, and if G is metacyclic then H is metacyclic.
On quasi-duo rings
Authors: Yu Hua-Ping
Published: May 2009

Bass [1] proved that if R is a left perfect ring, then R contains no infinite sets of orthogonal idempotents and every nonzero left R-module has a maximal submodule, and asked if this property characterizes left perfect rings ([1], Remark (ii), p. 470). The fact that this is true for commutative rings was proved by Hamsher [12], and that this is not true in general was demonstrated by examples of Cozzens [7] and Koifman [14]. Hamsher's result for commutative rings has been extended to some noncommutative rings. Call a ring left duo if every left ideal is two-sided; Chandran [5] proved that Bass’ conjecture is true for left duo rings. Call a ring R weakly left duo if for every r ε R, there exists a natural number n(r) (depending on r) such that the principal left ideal Rrn(r) is two-sided. Recently, Xue [21] proved that Bass’ conjecture is still true for weakly left duo rings.
On the idempotence and stability of kernel functors
Authors: Teply Mark L.
Published: May 2009

A kernel functor (equivalently, a left exact torsion preradical) is a left exact subfunctor of the identity on the category R-mod of left R-modules over a ring R with identity. A kernel functor is said to be idempotent if, in addition, σ satisfies σ(M / σ(M)) = 0 for every M ∊ R-mod. To every kernel functor / there corresponds a unique topologizing filter ℒσ = {I Ⅰ σ (R/I) = R/I} of left ideals and a unique class ℱσ = {M ∊ R-mod Ⅰ σ(M) = M} that is closed under homomorphic images, submodules, and direct sums. The idempotence of σ is characterized by either of the following additional conditions:

(1) if I ∊ ℒσ, K ⊆ I, and (K:x) = {r ∊ R ∣ rx ∊ K} ∊ ℒσ for each x ∊ I, then K ∊ ℒ or

(2) ℱσ is closed under extensions of one member of ℱσ by another member of ℱσ Idempotent kernel functors are important since they are the tool used to construct localization functors. For M∊ R-mod, let E(M) denote the injective hull of M. A kernel functor σ is called stable if Mℱ implies that E(M) ∊ ℱσ For more information about kernel functors, see [6], [7], [14], and [15].
Hilbert modules revisited: orthonormal bases and Hilbert-Schmidt operators
Authors: Cabrera M. , Martínez J. , Rodríguez A.
Published: May 2009

The concept of a Hilbert module (over an H*-algebra) arises as a generalization of that of a complex Hilbert space when the complex field is replaced by an (associative) H*-algebra with zero annihilator. P. P. Saworotnow [13] introduced Hilbert modules and extended to its context some classical theorems from the theory of Hilbert spaces, J. F. Smith [17] gave a complete structure theory for Hilbert modules, and G. R. Giellis [9] obtained a nice characteristization of Hilbert modules.
Cone characterization of reflexive Banach lattices
Authors: Polyrakis Ioannis A.
Published: May 2009

We prove that a Banach lattice X is reflexive if and only if X+ does not contain a closed normal cone with an unbounded closed dentable base.
Groups with finitely many conjugacy classes of subgroups with large subnormal defect
Authors: Smith Howard
Published: May 2009

Given a group G and a positive integer k, let vk(G) denote the number of conjugacy classes of subgroups of G which are not subnormal of defect at most k. Groups G such that vkG) < ∝ for some k are considered in Section 2 of [1], and Theorem 2.4 of that paper states that an infinite group G for which vk(G) < ∝ (for some k) is nilpotent provided only that all chief factors of G are locally (soluble or finite). Now it is easy to see that a group G whose chief factors are of this type is locally graded, that is, every nontrivial, finitely generated subgroup F of G has a nontrivial finite image (since there is a chief factor H/K of G such that F is contained in H but not in K). On the other hand, every (locally) free group is locally graded and so there is in general no restriction on the chief factors of such groups. The class of locally graded groups is a suitable class to consider if one wishes to do no more than exclude the occurrence of finitely generated, infinite simple groups and, in particular, Tarski p-groups. As pointed out in [1], Ivanov and Ol'shanskiĭ have constructed (finitely generated) infinite simple groups all of whose proper nontrivial subgroups are conjugate; clearly a group G with this property satisfies v1(G) = l. The purpose of this note is to provide the following generalization of the above-mentioned theorem from [1].
On reducibility of ultrametric almost periodic linear representations
Authors: Diarra Bertin
Published: May 2009

Let G be a group and K be a complete ultrametric valued field. Let AP(G, K) be the algebra of the generalized almost periodic functions of G in K. We have shown in a previous paper that when AP(G, K) has an invariant mean, then any almost periodic linear representation is quasi-reducible. Here, we show that with the same hypothesis, any topologically irreducible almost periodic linear representation is finite dimensional; also, any almost periodic linear representation is the topological sum of irreducible representations. Furthermore, we obtain a Peter-Weyl theorem for the algebra AP(G, K).

We use the technical tools of Hopf algebra theory.
On the nilpotent ranks of certain semigroups of transformations
Authors: Garba G. U.
Published: May 2009

Let Pn be the semigroup of all partial transformations on the set Xn = {1,…, n}. As usual, we shall say that an element α in Pn is of type (k, r) or belongs to the set [k, r] if |dom α|=k and |lim α|. The completion α* of an element α ∈ [n − 1, n − 1] is an element in [n, n] defined by

where {i} = Xn∖dom α and {j} = Xn∖im α.
Schottky uniformizations of closed Riemann surfaces with Abelian groups of conformal automorphisms
Authors: Hidalgo Rubén A.
Published: May 2009

Let us consider a pair (S, H) consisting of a closed Riemann surface S and an Abelian group H of conformal automorphisms of S. We are interested in finding uniformizations of S, via Schottky groups, which reflect the action of the group H. A Schottky uniformization of a closed Riemann surface S is a triple (Ώ, G, π:Ώ→S) where G is a Schottky group with Ώ as its region ofdiscontinuity and π:Ώ→S is a holomorphic covering with G ascovering group. We look for a Schottky uniformization (Ώ, G, π:Ώ→S) of S such that for each transformation h in H there exists an automorphisms t of Ώ satisfying h ∘ π = π ∘ t.
Conjugacy classes in sylow p-subgroups of GL(n, q), IV
Authors: Vera-López A. , Arregi J. M.
Published: May 2009

In this paper we give new information about the conjugacy vector of the group , the Sylow p-subgroup of GL(n, q) consisting of the upper unitriangular matrices. The first two components of this vector are given in [4]. Here, we obtain the third component, that is, the number of conjugacy classes whose centralizer has qn+l elements. Besides, we give the whole set of numbers which compose this vector:
Almost factorisable inverse semigroups
Authors: Lawson M. V.
Published: May 2009

In [3], McAlister introduced a class of semigroups, calledcovering semigroups, which were shown to play an important role in the theory ofE-unitary covers of semigroups. Strangely, this class of semigroups appears to have received little attention subsequently. It is the aim of this paper to rehabilitate them and to study their properties in more detail. As a first step, we have chosen to rename themalmost factorisable semigroups, since they can be regarded as the semigroup analogues of factorisable inverse monoids. Before discussing the contents of this paper in more detail we recall some standard terminology.
Polycyclic group rings and unique factorisation rings
Authors: MacKenzie Kenneth W.
Published: May 2009

The theory of unique factorisation in commutative rings has recently been extended to noncommutative Noetherian rings in several ways. Recall that an element x of a ring R is said to be normalif xR = Rx. We will say that an element p of a ring R is (completely) prime if p is a nonzero normal element of R and pR is a (completely) prime ideal. In [2], a Noetherian unique factorisation domain (or Noetherian UFD) is defined to be a Noetherian domain in which every nonzero prime ideal contains a completely prime element: this concept is generalised in [4], where a Noetherian unique factorisation ring(or Noetherian UFR) is defined as a prime Noetherian ring in which every nonzero prime ideal contains a nonzero prime element; note that it follows from the noncommutative version of the Principal Ideal Theorem that in a Noetherian UFR, if pis a prime element then the height of the prime ideal pR must be equal to 1. Surprisingly many classes of noncommutative Noetherian rings are known to be UFDs or UFRs: see [2] and [4] for details. This theory has recently been extended still further, to cover certain classes of non-Noetherian rings: see [3].
On reducible braids and composite braids
Authors: Humphries Stephen P.
Published: May 2009

The braid group on n strings Bn has a presentation as a group with generators σ1, …, σn−1 and relations
Classification of tensor product immersions which are of 1-type
Authors: Chen Bang-Yen
Published: May 2009

Let V and W be two vector spaces over the field of real numbers R. Then we have the notion of the tensor product V ⊗ W. If V and W are inner product spaces with their inner products given respectively by «,»v and «,» w, then V ⊗ W is also an inner product space with inner product denned by

Let Em denote the m-dimensional Euclidean space with the canonical Euclidean inner product. Then, with respect to the inner product defined above, Em ⊗Em is isometric to Em. By applying this algebraic notion, we have the notion of tensor product mapf ⊗h: M→ E: M ⊗= Em; associated with any two maps f: M→Em and h:M→E of a given Riemannian manifold (M, g) defined as follows:

Denote by R(M) the set of all transversal immersions from an n-dimensional Riemannian manifold (M, g) into Euclidean spaces; i. e., immersions f:M→Em with f(p) ∉T*(TPM) for p ∈ M. Then ⊗ is a binary operation on R(M). Hence, if f: Mm and h: M→Em are immersions belonging to R(M), then their tensor product map f ⊗ h: M→ Em ⊗ Em ≡ Emm is an immersion in R(M), called the tensor product immersionof f and h.
Local spectral theory and spectral inclusions
Authors: Laursen Kjeld B. , Neumann Michael M.
Published: May 2009

Suppose thatTandSare continuous linear operators on complex Banach spacesXandY, respectively, and thatAis a non-zero continuous linear mapping fromXtoY. IfAintertwinesTandSin the sense thatSA=AT, then a classical result due to Rosenblum implies that the spectra σ(T) and σ(S) must overlap, see [12]. Actually, Davis and Rosenthal [5]have shown that the surjectivity spectrum σsu(T) will meet the approximate point spectrum σap(S) in this case (terms to be denned below). Further information about the relations between the two spectra and their finer structure becomes available when the intertwinerAis injective or has dense range, see [9], [12], [13].
Defining-relations for Hurwitz groups
Authors: Campbell C. M. , Conder M. D. E. , Robertson E. F.
Published: May 2009

With much sadness we note the death of John Leech, on 28 September 1992. Perhaps best known for his discovery of the “Leech Lattice” (which provides the best known sphere-packing in 24 dimensions), John will also be remembered for his contributions to the use of computers in mathematics, and to computational algebra in particular.
Coranks of a quasi-projective module and its endomorphism ring
Authors: Takeuchi Tsutomu
Published: May 2009

Recently several authors have studied dualizing Goldie dimension of a module: spanning dimension in [2], codimension in [13], corank in [16] and also [9,17,12, 5,11, 6, 4, 7] ([13] may be read in comparison with the others). In the present note we prove the equality corankRP= corankSS, wherePis a quasi-projective leftR-module andSis its endomorphism ring. This result is an answer to the question [12, p. 1898] and an extension of [3, Corollary 4.3] which shows the above equality for a Σ-quasi-projective leftR-moduleP.
Capitulation in unramified quadratic extensions of real quadratic number fields
Authors: Benjamin E. , Sanborn F. , Snyder C.
Published: May 2009

Letkbe an algebraic number field andCkits ideal class group (in the wider sense). SupposeKis a finite extension ofk. Then we say that an ideal class ofk capitulatesinKif this class is in the kernel of the homomorphism

induced by extension of ideals fromktoK(See Section 2 below). In [4], Iwasawa gives examples of real quadratic number fields,with distinct primesPi≡ 1 (mod 4), for which all the ideal classes of the 2-class group,Ck,2(the 2-Sylow subgroup ofCk), capitulate in an unramified quadratic extension ofk. In these examples,Ck,2is abelian of type (2,2), i.e. isomorphic to ℤ/2ℤ×ℤ/2ℤ and so all four ideal classes capitulate.
A Mayer-Vietoris sequence in group homology and the decomposition of relation modules
Authors: Duncan A. J. , Ellis Graham J. , Gilbert N. D.
Published: May 2009

W. A. Bogley and M. A. Gutierrez [2] have recently obtained an eight-term exact homology sequence that relates the integral homology of a quotient group Г/MN, where M and N are normal subgroups of the group Г, to the integral homology of the free product Г/M * Г/N in dimensions ≤3 by means of connecting terms constructed from commutator subgroups of Г, M, N and M ∩ N. In this paper we use the methods of [4] to recover this exact sequence under weaker hypotheses and for coefficients in /q for any non-negative integer q. Further, for q = 0 we extend the sequence by three terms in order to capture the relation between the fourth homology groups.
On the endomorphism semigroup of an ordered set
Authors: Blyth T. S.
Published: May 2009

M. E. Adams and Matthew Gould [1] have obtained a remarkable classification of ordered sets P for which the monoid End P of endomorphisms (i.e. isotone maps) is regular, in the sense that for every f є End P there exists g є End P such that fgf = f. They show that the class of such ordered sets consists precisely of

(a) all antichains;

(b) all quasi-complete chains;

(c) all complete bipartite ordered sets (i.e. given non-zero cardinals α β an ordered set Kα,β of height 1 having α minimal elements and β maximal elements, every minimal element being less than every maximal element);

(d) for a non-zero cardinal α the lattice Mα consisting of a smallest element 0, a biggest element 1, and α atoms;

(e) for non-zero cardinals α, β the ordered set Nα,β of height 1 having α minimal elements and β maximal elements in which there is a unique minimal element α0 below all maximal elements and a unique maximal element β0 above all minimal elements (and no further ordering);

(f) the six-element crown C6 with Hasse diagram

A similar characterisation, which coincides with the above for sets of height at most 2 but differs for chains, was obtained by A. Ya. Aizenshtat [2].
Polynomial Grothendieck properties
Authors: González Manuel , Gutiérrez Joaquí M.
Published: May 2009

A Banach space sE has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space (kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric A>fold projective tensor product of £(i.e., the predual of (kE)) having the Grothendieck property. The Grothendieck property of the projective tensor product EF is also characterized. Moreover, the Grothendieck property of E is described in terms of sequences of polynomials. Finally, it is shown that if every operator from E into c0 is completely continuous, then so is every polynomial between these spaces.
Null 2-type Chen surfaces
Authors: Li Shi-Jie
Published: May 2009

Let M be an n-dimensional connected submanifold in an mdimensional Euclidean space Em. Denote by δ the Laplacian of M associated with the induced metric. Then the position vector x and the mean curvature vector H of Min Em satisfy

This yields the following fact: a submanifold M in Em is minimal if and only if all coordinate functions of Em, restricted to M, are harmonic functions. In other words, minimal submanifolds in Emare constructed from eigenfunctions of δ with one eigenvalue 0. By using (1. 1), T. Takahashi proved that minimal submanifolds of a hypersphere of Em are constructed from eigenfunctions of δ with one eigenvalue δ (≠0). In [3, 4], Chen initiated the study of submanifolds in Em which are constructed from harmonic functions and eigenfunctions of δ with a nonzero eigenvalue. The position vector x of such a submanifold admits the following simple spectral decomposition:

for some non-constant maps x0and xq, where A is a nonzero constant. He simply calls such a submanifold a submanifold of null 2-type.
Outer automorphisms of hypercentral p-groups
Authors: Puglisi Orazio
Published: May 2009

In his celebrated paper [3] Gaschiitz proved that any finite non-cyclic p-group always admits non-inner automorphisms of order a power of p. In particular this implies that, if G is a finite nilpotent group of order bigger than 2, then Out (G) = Aut(G)/Inn(G) =≠1. Here, as usual, we denote by Aut (G) the full group of automorphisms of G while Inn (G) stands for the group of inner automorphisms, that is automorphisms induced by conjugation by elements of G. After Gaschiitz proved this result, the following question was raised: “if G is an infinite nilpotent group, is it always true that Out (G)≠1?”
The 3-local cohomology of the Mathieu group M24
Authors: Green David John
Published: May 2009

In this paper we calculate the localisation at the prime 3 of the integral cohomology ring of the Mathieu group M24, together with its mod-3 cohomology ring. The main results are

Theorem 1. The ring H*(M24, Z)(3)is the commutative graded Z(3)-algebra with generators

and relations v2 = 0 and βθ = 0. The Chern classes of the Todd representation in GL11F2
The range of non-surjective convolution operators on Beurling spaces
Authors: Bonet José , Galbis Antonio
Published: May 2009

Let μ ≠ 0 be an ultradistribution of Beurling type with compact support in the space . We investigate the range of the convolution operator Tμ on the space of non-quasianalytic functions of Beurling type associated with a weight w, in the case the operator is not surjective. It is proved that the range of TM always contains the space of real-analytic functions, and that it contains a smaller space of Beurling type for a weight σ ≥ ω if and only if the convolution operator is surjective on the smaller class.
On the theorem of Wójcik
Authors: Rotkiewicz A.
Published: May 2009

In the paper [3] the following lemma was proved.

Lemma. Let a, b and c be positive integers such that a and be are relatively prime. Then there are infinitely many primes p in the arithmetic progression ax + b (x = 0,1,2,…) such that
Solutions of Diophantine equations and divisibility of class numbers of complex quadratic fields
Authors: Mollin R. A.
Published: May 2009

We show how the solution to certain diophantine equations involving the discriminant of complex quadratic fields leads to the divisibility of the class numbers of the underlying fields. This not only generalizes certain results in the literature such as [2], [4]–[6] but also shows why certain hypotheses made in these results are actually unnecessary since, as our criteria demonstrate, these hypotheses are forced by the solution of the diophantine equations involved. Our methods are based only on the most elementary properties of a principal ideal in a complex quadratic field.
On a hyperlogistic delay equation
Authors: Yu Jianshe , Wu Jianhong , Zou Xingfu
Published: May 2009

Consider the following hyperlogistic equation

wherer, K, τj∈ (0, ∝), and αj=pj/qjare rational numbers withqjodd,pjandqj, are co-prime, 1 ≤j≤m, and.
Standard prime ideals and lying over for finite extensions of Noetherian algebras
Authors: Krause Günter
Published: May 2009

Let k be a field, let R be a noetherian k-algebra of finite Gelfand-Kirillov dimension GK(R), and let M be a finitely generated right R-module. A standard prime factor series for M is a finite sequence of submodules 0 = N0 ⊂ N1 ⊂…⊂ Ni−1 ⊂ Ni ⊂.… ⊂ Nn = M, such that for each i the annihilator Pi = rR (Ni/Ni−1) is the unique associated prime of Ni/Ni−1 and GK(R/Pi)≤ GK(R/Pj) whenever i≤ j. The set of prime ideals arising from such a series is an invariant of M, called the set of standard primes St(M) of M. The concept, inspired by the notion of a standard affiliated series introduced by Lenagan and Warfield in [7], has been developed in [5], where it was shown that St(M) coincides with the set of all those prime ideals that are minimal over the annihilator of a nonzero submodule of M.
An integral formula for hypersurfaces in space forms
Authors: Vlachos Theodoros
Published: May 2009

Let be an n+ 1-dimensional, complete simply connected Riemannian manifold of constant sectional curvature c and We consider the function r(·) = d(·, P0) where d stands for the distance function in and we denote by grad r the gradient of The position vector (see [1]) with origin P0 is defined as where ϕ(r)equals

r, if c = 0, c< 0 or c <0 respectively.
On p-injective rings
Authors: Puninski Gennadi , Wisbauer Robert , Yousif Mohamed
Published: May 2009

Throughout this paper R will be an associative ring with unity and all R-modules are unitary. The right (resp. left) annihilator in R of a subset X of a module is denoted by r(X)(resp. I(X)). The Jacobson radical of R is denoted by J(R), the singular ideals are denoted by Z(RR) and Z(RR) and the socles by Soc(RR) and Soc(RR). For a module M, E(M) and PE(M) denote the injective and pure-injective envelopes of M, respectively. For a submodule A ⊆ M, the notation A ⊆⊕M will mean that A is a direct summand of M.
Finite groups of outer automorphisms of free groups
Authors: Zimmermann Bruno
Published: May 2009

Let Fr denote the free group of rank r and Out Fr: = AutFr/Inn Fr the outer automorphism group of Fr (automorphisms modulo inner automorphisms). In [10] we determined the maximal order 2rr! (for r > 2) for finite subgroups of Out Fr as well as the finite subgroup of that order which, for r > 3, is unique up to conjugation. In the present paper we determine all maximal finite subgroups (that is not contained in a larger finite subgroup) of Out F3, up to conjugation (Theorem 2 in Section 3). Here the considered case r = 3 serves as a model case: our method can be applied for other small values of r (in principle for any value of r) but the computations become considerably longer and are more apt for a computer then; the method can also be applied to determine the maximal finite subgroups of the automorphism group Aut Fr of Fr. Note that the canonical projection Aut Fr ⃗ Out Fr is injective on finite subgroups of Aut Fr; however, not all finite subgroups of Out Fr lift to finite subgroups of Aut Fr.
Complete submanifolds with parallel mean curvature in a sphere
Authors: Vlachos Theodoros
Published: May 2009

Let Mn be an n-dimensional manifold immersed in an (n+p)-dimensional unit sphere Sn+p, with mean curvature H and second fundamental form B. We put φ(X, Y) = B(X, Y)–(X, Y)H where X and Y are tangent vector fields on Mn. Assume that the mean curvature is parallel in the normal bundle of Mn in Sn+p. Following Alencar and do Carmo [1] we denote by BH the square of the positive root of
Normal curvature of minimal submanifolds in a sphere
Authors: Deshmukh Sharief
Published: May 2009

Simons [5] has proved a pinching theorem for compact minimal submanifolds in a unit sphere, which led to an intrinsic rigidity result. Sakaki [4] improved this result of Simons for arbitrary codimension and has proved that if the scalar curvature S of the minimal submanifold Mn of Sn+P satisfies

then either Mn is totally geodesic or S= 2/3 in which case n = 2 and M2 is the Veronese surface in a totally geodesic 4-sphere. This result of Sakaki was further improved by Shen [6] but only for dimension n=3, where it is shown that if S>4, then M3 is totally geodesic (cf. Theorem 3, p. 791).
On the adjoint group of some radical rings
Authors: Dickenschied Oliver
Published: May 2009

A ring R is called radical if it coincides with its Jacobson radical, which means that Rforms a group under the operation a ° b = a + b + ab for all a and b in R. This group is called the adjoint group R° of R. The relation between the adjoint group R° and the additive group R+ of a radical rin R is an interesting topic to study. It has been shown in [1] that the finiteness conditions “minimax”, “finite Prufer rank”, “finite abelian subgroup rank” and “finite torsionfree rank” carry over from the adjoint group to the additive group of a radical ring. The converse is true for the minimax condition, while it fails for all the other above finiteness conditions by an example due to Sysak [6] (see also [2, Theorem 6.1.2]). However, we will show that the converse holds if we restrict to the class of nil rings, i.e. the rings R such that for any a є R there exists an n = n(a) with an = 0.
Jacobi elliptic algebras of SO(3)
Authors: Myung Hyo Chul , Lee Dong Soo
Published: May 2009

A class of algebras that describe invariant pseudo-Riemannian connections on SO(3) is shown to comprise Jacobi elliptic algebras arising from the Jacobi elliptic functions
On the distribution of αpk modulo 1
Authors: Wong K. C.
Published: May 2009

The fractional part of the sequence {αnk}, where α is an irrational real number and k is an integer, was first studied early this century, initiated by the work of Hardy, Littlewood and Weyl. It seems very natural to consider the subsequence {αpk}, where p denotes a prime variable. The pioneering work in this direction was conducted by Vinogradov [13,14]. Improvements have since been made by Vaughan [12], Ghosh [4], Harman [6,7,8] and Jia [11]. The best results to date have been obtained by Harman for k = 1 [9], by Baker and Harman for 2 ≤ k ≤ 12 [1], and by Harman for larger k [8]. In the following work, we shall adopt a sieve technique developed by Harman in [6] to show the following.
Groups with few non-nilpotent subgroups
Authors: Smith Howard
Published: May 2009

Let G be a non-nilpotent group in which all proper subgroups are nilpotent. If G is finite then G is soluble [18], and a classification of such groups is given in [14]. The paper [12]. of Newman and Wiegold discusses infinite groups with this property. Clearly such a group is either finitely generated or locally nilpotent. Many interesting results concerning the finitely generated case are established in [12]. Since the publication of that paper there have appeared the examples due to Ol'shanskii and Rips (see [13]) of finitely generated infinite simple p-groups all of whose proper nontrivial subgroups have order p, a prime. Following [12], let us say that a group G is an AN-group if it is locally nilpotent and non-nilpotent with all proper subgroups nilpotent. A complete description is given in Section 4 of [12] of AN-groups having maximal subgroups. Every soluble AN-gvoup has locally cyclic derived factor group and is a p-group for some prime p ([12; Lemma 4.2]). The only further information provided in [12] on AN-groups without maximal subgroups is that they are countable. Four years or so after the publication of [12], there appeared the examples of Heineken and Mohamed [5]: for every prime p there exists a metabelian, non-nilpotent p-group G having all proper subgroups nilpotent and subnormal; further, G has no maximal subgroups and so G/G' is a Prüfer p-group in each case.
Measurable majorants in L1
Authors: Lambert Alan
Published: May 2009

Given a probability space (X, ℱ, μ) and a σ-algebra A ⊂ ℱ, arguably the most powerful tool in gaining information about an ℱ-measurable function f from restricted knowledge of -measurability is that of the conditional expectation E(f | ); written throughout the remainder of this note. Two properties of conditional expectation that may be exploited to gain information, but which also limit conditional expectation's use are the following.
Basis of quadratic differentials for Riemann surfaces with automorphisms
Authors: Riera Gonzalo
Published: May 2009

The uniformization theorem says that any compact Riemann surface S of genus g≥2 can be represented as the quotient of the upper half plane by the action of a Fuchsian group A with a compact fundamental region Δ.
Weyl's theorem holds for p-hyponormal operators
Authors: Chō Muneo , Itoh Masuo , Ōshiro Satoru
Published: May 2009

Let ℋ be a complex Hilbert space and B(ℋ) the algebra of all bounded linear operators on ℋ. Let ℋ(ℋ) be the algebra of all compact operators of B(ℋ). For an operator T ε B(ℋ), let σ(T), σp(T), σπ(T) and πoo(T) denote the spectrum, the point spectrum, the approximate point spectrum and the set of all isolated eigenvalues of finite multiplicity of T, respectively. We denote the kernel and the range of an operator T by ker(T) and R(T), respectively. For a subset of ℋ, the norm closure of is denoted by . The Weyl spectrum ω(T) of T ε B(ℋ) is defined as the set
A family of conformally asymmetric Riemann surfaces
Authors: Everitt Brent
Published: May 2009

We give explicit examples of asymmetric Riemann surfaces (that is, Riemann surfaces with trivial conformal automorphism group) for all genera g ≥ 3. The technique uses Schreier coset diagrams to construct torsion-free subgroups in groups of signature (0; 2,3,r) for certain values of r.