bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Brown Mccoy radical of semigroup rings of commutative cancellative semigroups
Authors: Jespers E. , Krempa J. , Wauters P. 
Published: May 2009

We give a complete description of the Brown–McCoy radical of a semigroup ring R[S], where R is an arbitrary associative ring and S is a commutative cancellative semigroup; in particular we obtain the answer to a question of E. Puczyłowski stated in [11]Throughout this note all rings R are associative with unity 1; all semigroups S are commutative and cancellative with unity. Note that the condition that R and S have a unity can be dropped (cf. [8]). The quotient group of S is denoted by Q(S). We say that S is torsion free (resp. has torsion free rank n) if Q(S) is torsion free (resp. has torsion free rank n). The Brown–McCoy radical (i.e. the upper radical determined by the class of all simple rings with unity) of a ring R is denoted by u(R). We refer to [2] for further detail on radicals and in particular on the Brown–McCoy radical.First we state some well-known results and a preliminary lemma. Let R and T be rings with the same unity such that R ⊂ T. Then T is said to be a normalizing extension of R if T = Rx1+…+Rxn for certain elements x1, …, xn of T and Rxi = xiR for all i such that 1 ∨i∨n. If all xi are central in T, then we say that T is a central normalizing extension of R.
A diophantine equation
Authors: Cassels J. W. S. 
Published: May 2009

I was recently challenged to find all the cases when the sum of three consecutive integral cubes is a square; that is to find all integral solutions x, y ofy2=(x−1)3+x3+(x+1)3=3x(x2+2)This is an example of a curve of genus 1. There is an effective procedure for finding all integral points on a given curve of genus 1 ([1, Theorem 4.2], [2]): that is, it can be guaranteed to find all the integral points and to show that no others exist with a finite amount of work. Unlike some effective procedures, which have only logical interest, this one can actually be carried out in practice, at least with the aid of a computer ([3], [5]). There are, however, older methods for dealing with problems of this kind which, while not effective, very often lead more easily to a complete set of solutions (and a proof that it is complete). I solve the problem here by a technique introduced in [4]. It requires only the elementary theory of algebraic number–fields. The motivation is p–adic, but it is simpler not to introduce p–adic theory overtly.
On the spectrum of an integral operator
Authors: Rooney P. G. 
Published: May 2009

The integral operator which we will consider in this paper is the operator T denned for suitably restricted functions f on (0, ∞) bywhere x >0 and the integral is taken in the Cauchy principal value sense at t = x. This operator plays a considerable role in Wiener–Hopf theory; see [2; Chapter 5].Since T is clearly the restriction to (0, ∞) of minus the Hilbert transformation applied to functions which vanish on (−∞, 0), it follows easily from the theory of the Hilbert transformation, as given in say [6; Theorem 101], that T is a bounded operator from Lp(0, ∞) to itself for 1 < p < ∞.
A theorem on polynomial lorentz structures
Authors: Deszyński Krzysztof 
Published: May 2009

Let M be a differentiable manifold of dimension m. A tensor field f of type (1, 1) on M is called a polynomial structure on M if it satisfies the equation:where a1, a2, …, an are real numbers and I denotes the identity tensor of type (1, 1).We shall suppose that for any x ∈ Mis the minimal polynomial of the endomorphism fx: TxM → TxM.We shall call the triple (M, f, g) a polynomial Lorentz structure if f is a polynomial structure on M, g is a symmetric and nondegenerate tensor field of type (0, 2) of signaturesuch that g (fX, fY) = g(X, Y) for any vector fields X, Y tangent to M. The tensor field g is a (generalized) Lorentz metric.
On a theorem of Dvoretsky, Wald, and Wolfowitz concerning Liapounov Measures
Authors: Edwards D. A. 
Published: May 2009

Let ω be a non-empty set, ℱ a Boolean σ-algebra of subsets of Ω, k a natural number, and let m:ℱ→ℝk be a non-atomic vector measure. Then, by the celebrated theorem of Liapounov [11], the range m[3F] = {m(A): A ε ℱ3F} of m is a compact convex subset of ℝk. This theorem has been generalized in a number of ways. For example Kingman and Robertson [8] and Knowles [9] have shown that, under appropriate conditions, results in the same spirit can be proved for measures taking their values in infinite-dimensional vector spaces. Another type of generalization was obtained by Dvoretsky, Wald and Wolfowitz [6,7]. What they do is to take m as above together with a natural number n≥ 1. They then consider the set Knof all vectorswhere (A1 A2,…, An) is an ordered ℱ-measurable partition of Ω (i.e. a partition whose terms A, all belong to ℱ). They prove in [6] that Kn is a compact convex subset of ℝnk and moreover that Kn is equal to the set of all vectors of the formwhere (ϕ1, ϕ2…, ϕn) is an ℱ-measurable partition of unity; i.e. it is an n-tuple of non-negative ϕr on Ω such thatLiapounov's theorem can be obtained as a corollary of this result by taking n= 2.
Bisimple weakly inverse semigroups with partial right unitoids
Authors: Madhavan S. 
Published: May 2009

In an earlier paper [5] of the author bisimple weakly inverse semigroups with partial identities were studied. The aim of this paper is to extend the results to a wider class of semigroups, viz: bisimple weakly inverse semigroups with partial right unitoids. It is found that an ℛ-class of weakly inverse semigroup is a right skew groupoid R = (R, P), where P is a right skew semigroup [5], P⊆R, and R is a partial semigroup satisfying certain conditions. When S is a bisimple weakly inverse semigroup with E the set of partial right unitoids, it can be shown that the ℛ-class R = (R, P) containing E, which is a right skew groupoid, satisfies the following:(i) for any a, b ∈ R, there exists c ∈ R such that Pa ∩ Pb = Pc;(ii) for any a ∈ R, there exists a left identity e of R such that (Pa ∩ P)e = Pa ∩ P.
Continuity and differentiability properties of the Nemitskii operator in Hölder spaces
Authors: Nugari Rita 
Published: May 2009

Let ℝn be the n-dimensional Euclidean space with the usual norm denoted by |·| In what follows 蒆 will denote an open bounded subset of ℝn, and its closure.For α ∊(0,1], is the space of all functions such that: is called the Holder space with exponent a and is a Banach space when endowed with the norm:where ‖u‖∞ is, as usual, defined by:
Minimal theta functions
Authors: Montgomery Hugh L. 
Published: May 2009

Let be a positive definite binary quadratic form with real coefficients and discriminant b2 − 4ac = −1.Among such forms, let . The Epstein zeta function of f is denned to beRankin [7], Cassels [1], Ennola [5], and Diananda [4] between them proved that for every real s > 0,We prove a corresponding result for theta functions. For real α > 0, letThis function satisfies the functional equation(This may be proved by using the formula (4) below, and then twice applying the identity (8).)
Topological types of Klein surfaces with a maximum order automorphism
Authors: Bujalance J. A. 
Published: May 2009

If X is a Klein surface (KS) with boundary, of algebraic genus p, and Φ is an automorphism of order N, May [8] proved that N ≤ 2p + 2 when X is orientable and p is even, and N ≤ 2p otherwise.He proved also that the unique topological type of an orientable KS having an orientation-preserving automorphism of maximum order is a surface with one boundary component when p is even, with two boundary components when p is odd.
On the degrees of projective representations
Authors: Higgs R. J. 
Published: May 2009

All representations and characters studied in this paper are taken over the complex numbers, and all groups considered are finite. For basic definitions concerning projective representations see [1].If G is a group and or is a cocycle of G we denote by Proj(G, α) = {ξ1, …, ξt} the set of irreducible projective characters of G with cocycle α, where of course t is the number of α-regular conjugacy classes of G; ξ1, (1) is called the degree of ξ1. Also as normal, M(G) will denote the Schur multiplier of G, [α] the cohomology classof α, and [1] the cohomology class of the trivial cocycle of G.
Groups whose Projective character degrees are powers of a prime
Authors: Higgs R. J. 
Published: May 2009

Let Gbe a finite group, and P:G → GL(n, ) be such that for all x, y ∈ G(i) P(x)P(y) = α(x, y)P(xy), and(ii)P(l) = In,where α(x, y) ∈ *; then P is a projective representation of G with cocycle α and degree n. For other basic definitions concerning projective representations see [4].
Representations of rank one algebraic monoids
Authors: Renner Lex E. 
Published: May 2009

One of the fundamental results of representation theory is the identification of the irreducible representations of a semisimple group by their dominant weights [3]. The purpose of this paper is to establish similar results for a class of reductive algebraic monoids.Let k be an algebraically closed field. An algebraic monoid is an affine algebraic variety M defined over k, together with an associative morphism m:M × M → M and a two-sided unit 1 ∈ M for m.
A uniqueness theorem for harmonic functions on half-spaces
Authors: Armitage D. H. 
Published: May 2009

An arbitrary point of the Euclidean space Rn+1, where n > 1, is denoted by (X, y), where X ∈ Rn and y ∈ R, and we denote the Euclidean norm on Rn by ∥·∥. If h is harmonic on the half-space Ω = {(X, y): y > 0}, then we define extended real-valued functions m and M as follows:and
Relation modules of amalgamated free products and HNN extensions
Authors: Hannebauer Torsten 
Published: May 2009

Let G be a group anda free presentation of G, i.e. a short exact sequence of groups with F free. Conjugation in F induces on = R/R', the abelianized normal subgroup R, the structure of a right G-module (if r∈ R, x∈ F then (r)(xπ) = x-1rxR'). The G-module is called the relation module determined by the presentation (1). For a detailed discussion of this subject we refer to Gruenberg [3].
Separability of the L1-space of a vector measure
Authors: Ricker Werner J. 
Published: May 2009

Let Σ be a σ-algebra of subsets of some set Ω and let μ:Σ→[0,∞] be a σ-additive measure. If Σ(μ) denotes the set of all elements of Σ with finite μ-measure (where sets equal μ-a.e. are identified in the usual way), then a metric d can be defined in Σ(μ) by the formulahere E ΔF = (E\F) ∪ (F\E) denotes the symmetric difference of E and F. The measure μ is called separable whenever the metric space (Σ(μ), d) is separable. It is a classical result that μ is separable if and only if the Banach space L1(μ), is separable [8, p.137]. To exhibit non-separable measures is not a problem; see [8, p. 70], for example. If Σ happens to be the σ-algebra of μ-measurable sets constructed (via outer-measure μ*) by extending μ defined originally on merely a semi-ring of sets Γ ⊆ Σ, then it is also classical that the countability of Γ guarantees the separability of μ and hence, also of L1(μ), [8, p. 69].
Left orders in regular ℋ-Semigroups II
Authors: Gould Victoria 
Published: May 2009

We make the convention that if a is an element of a semigroup Q then by writing a–1 it is implicit that a lies in a subgroup of Q and has inverse a–1 in this subgroup; equivalently, a ℋ a2 and a–1 is the inverse of a in Ha.A subsemigroup S of a semigroup Q is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be written as a–1b where a, b ∈ S and, in addition, every element of S satisfying a weak cancellation condition which we call square-cancellable lies in a subgroup of Q. The notions of right order and semigroup of right quotients are defined dually; if S is both a left order and a right order in Q then S is an order in Q and Q is a semigroup of quotients of S.
Tilting modules and a theorem of Hoshino
Authors: Assem Ibrahim , Kerner Otto 
Published: May 2009

Let k be an algebraically closed field, and A a finite dimensional k-algebra, which we shall assume, without loss of generality, to be basic and connected. By module is meant throughout a finitely generated right A-module. Following Happel and Ringel [10], we shall say that a module Tλ is a tilting (respectively, cotilting) module if it satisfies the following three conditions:(1)(2)(3) the number of non-isomorphic indecomposable summands of T equals the rank of the Grothendieck group K0(A) of A.
Finite abelian actions on surfaces
Authors: Jassim S. A. 
Published: May 2009

Let G be a finite abelian group of rank m, M an oriented compact connected surface, and F(G, M) the set of all orientation preserving free G-actions on M. Two actions φ1, φ2εF(G, M) are equivalent if there exists an orientation preserving homeomorphism h of M such thathφ1(f) for all f ε G.
Characterizations of Schützenberger graphs in terms of their automorphism groups and fundamental groups
Authors: Cowan David , Reilly Norman R. 
Published: May 2009

AbstractThe importance of the fundamental group of a graph in group theory has been well known for many years. The recent work of Meakin, Margolis and Stephen has shown how effective graph theoretic techniques can be in the study of word problems in inverse semigroups. Our goal here is to characterize those deterministic inverse word graphs that are Schutzenberger graphs and consider how deterministic inverse word graphs and Schutzenberger graphs can be constructed from subgroups of free groups.
On frattini-like subgroups
Authors: Beidleman James C. , Smith Howard 
Published: May 2009

Theorem 3 of the paper, published in the Glasgow Mathematical Journal 35 (1993), 95–98, is stated incorrectly.The subgroup G′ ∩ L(G) is nilpotent but not, in general, finitely generated (a suitable counterexample being provided by the group whose presentation is given n the Introduction). In groups with the property σ the Fitting radical is itself finitely generated and so the conclusion of Theorem 3 holds in this special case. The words “finitely generated” should be deleted from the paragraph preceding the statement of Theorem 4, but both this theorem and its proof are correct.
Lacunarity of Dedekind η-products
Authors: Gordon Basil , Robins Sinai 
Published: May 2009

The Dedekind η-function is defined bywhere τ lies in the upper half plane ℋ = {tau;|Im(τ) > 0}, and x = e2πiτ. It is a modular form of weight ½ with a multiplier system. We define an η-product to be a function f (τ) of the formwhere rδ ε ℤ. This is a modular form of weight with a multiplier system. The Fourier coefficients of η-products are related to many well-known number-theoretic functions, including partition functions and quadratic form representation numbers. They also arise from representations of the “monster” group [3] and the Mathieu group M24 [13]. The multiplicative structure of these Fourier coefficients has been extensively studied. Recent papers include [1], [4], [5] and [6]. Here we study the connections between the density of the non-zero Fourier coefficients of f(τ) and the representability of f(τ) as a linear combination of Hecke character forms (defined in Section 4 below). We first make the following definition.
Extension of completely bounded A-B bimodule maps
Authors: Muhly Paul S. , Na Qiyuan 
Published: May 2009

AbstractIn this paper, we present an “order” characterization of completely bounded bimodule maps for bimodules over unital operator algebras. We use this result to prove a bimodule generalization of Wittstock's generalized Hahn-Banach theorem. Our proofs simplify and unify some of Wittstock's arguments.
A weaker condition for normality
Authors: Doust Ian 
Published: May 2009

One of the most important results of operator theory is the spectral theorem for normal operators. This states that a normal operator (that is, a Hilbert space operator T such that T*T= TT*), can be represented as an integral with respect to a countably additive spectral measure,Here E is a measure that associates an orthogonal projection with each Borel subset of ℂ. The countable additivity of this measure means that if x Eℋ can be written as a sum of eigenvectors then this sum must converge unconditionally.
On the non-albelian tensor square of a nilpotent group of class two
Authors: Bacon Michael R. 
Published: May 2009

The nonabelian tensor square G⊗G of a group G is generated by the symbols g⊗h, g, h ∈ G, subject to the relations,for all g, g′, h, h′ ∈ G, where The tensor square is a special case of the nonabelian tensor product which has its origins in homotopy theory. It was introduced by R. Brown and J. L. Loday in [4] and [5], extending ideas of Whitehead in [6].
Modulus of nearly uniform smoothness and Lindenstrauss formulae
Authors: Benavides Tomás Domínguez 
Published: May 2009

AbstractThe Lindenstrauss formulawhich states a strong relationship between the (Clarkson) modulus of uniform convexity δx of a Banach space X and the modulus of uniform smoothness px* of the conjugate space X*, is well known. Following the idea of the definitions of nearly uniform smooth space by S. Prus and modulus of uniform smoothness we define a modulus of nearly uniform smoothness and prove some Lindenstrauss type formulae concerning this modulus and the modulus of nearly uniform convexity for some measures of noncompactness.
Right fully idempotent rings need not be left fully idempotent
Authors: Andruszkiewicz R. R. , Puczyłowski E. R. 
Published: May 2009

All rings in this paper are associative but not necessarily with an identity. The ring R with an identity adjoined will be denoted by R#.To denote that I is an ideal (right ideal, left ideal) of a ring R we write I ◃ R (I <rR, I <1R).A ring R is called right (left) fully idempotent if for every I <rR (I<1R), I = I2.At the conference “Methoden der Modul und Ringtheorie” in Oberwolfach, Germany in 1993, J. Clark raised the question as to whether every right fully idempotent ring is left fully idempotent (see also [3]). A similar question was raised by S. S. Page in [5]. In this note we answer the questions in the negative.We start with some general observations most of which are perhaps well known. We include their simple proofs for completeness.
On the diophantine equations x2 + 74 = y5 and x2 + 86 = y5
Authors: Mignotte Maurice , de Weger Benjamin M. M. 
Published: May 2009

AbstractJ. H. E. Cohn solved the diophantine equations x2 + 74 = yn and x2 + 86 = yn, with the condition 5 ∤ n, by more or less elementary methods. We complete this work by solving these equations for 5 | n, by less elementary methods.
On the topological degree of real polynomial vector fields
Authors: Szafraniec Zbigniew 
Published: May 2009

Let G: Rn → Rn be a continuous mapping such that the origin 0 ∈ Rn is isolated in G-1(0). Then deg0G will denote the local topological degree of G at the origin, i.e. the topological degree of the mappingwhere Sr denotes a sphere in Rn centered at the origin with small radius r > 0.
Some remarks on the p-homotopy type of B∑p2
Authors: Brunetti Maurizio 
Published: May 2009

Let G be a finite group, H a copy of its p-Sylow subgroup, and N the normalizer of H in G. A theorem by Nishida [10] states the p-homotopy equivalence of suitable suspensions of BN and BG when H is abelian. Recently, in [3] the authors proved a stronger result: let ΩkH be the subgroup of H generated by elements of order pk or less; ifthen BN and BG are stably p-homotopy equivalent. The hypothesis above is obviously verified when H is abelian. In the same paper the authors recall that H does not verify such condition when p = 2 and G = SL2(Fq) for a suitable odd prime power q; in this case BG and BN are not stably 2-homotopy equivalent.
Endomorphism regular Ockham algebras of finite Boolean type
Authors: Blyth T. S. , Silva H. J. 
Published: May 2009

AbstractIf (L; ƒ) is an Ockham algebra with dual space (X; g), then it is known that the semigroup of Ockham endomorphisms onLis (anti-)isomorphic to the semigroup Λ(X; g) of continuous order-preserving mappings onXthat commute withg. Here we consider the case whereLis a finite boolean lattice and ƒ is a bijection. We begin by determining the size of Λ(X;g), and obtain necessary and sufficient conditions for this semigroup to be regular or orthodox. We also describe its structure when it is a group, or an inverse semigroup that is not a group. In the former case it is a cartesian product of cyclic groups and in the latter a cartesian product of cyclic groups each with a zero adjoined.
Matched pairs of Lie algebroids
Authors: Mokri Tahar 
Published: May 2009

AbstractWe extend to Lie algebroids the notion variously known as a double Lie algebra (Lu and Weinstein), matched pair of Lie algebras (Majid), or twilled extension of Lie algebras (Kosmann-Schwarzbach and Magri). It is proved that a matched pair of Lie groupoids induces a matched pair of Lie algebroids. Conversely, we show that under certain conditions a matched pair of Lie algebroids integrates to a matched pair of Lie groupoids. The importance of matched pairs of Lie algebroids has been recently demonstrated by Lu.
Pietsch integral operators defined on injective tensor products of spaces and applications
Authors: Popa Dumitru 
Published: May 2009

AbstractFor X and Y Banach spaces, let X⊗εY, be the injective tensor product. If Z is also a Banach space and U ∊ L(X⊗εY,Z) we consider the operatorWe prove that if U ∊ PI(X⊗εY, Z), then U# ∊ I(X, PI(Y,Z)). This result is then applied in the case of operators defined on the space of all X-valued continuous functions on the compact Hausdorff space T. We obtain also an affirmative answer to a problem of J. Diestel and J. J. Uhl about the RNP property for the space of all nuclear operators; namely if X* and Y have the RNP and Y can be complemented in its bidual, then N(X, Y) has the RNP.
Montel subspaces of Fréchet spaces of Moscatelli type
Authors: Albanese Angela A. 
Published: May 2009

In this note we show that every complemented Montel subspace F of a Fréchet space E of Moscatelli type is isomorphic to ω or is finite–dimensional; the last case always occurs when E has a continuous norm. To do this, we first study the topology induced by E on its Montel subspaces, extending a result on Fr6chet-Montel spaces of Moscatelli type in [4].We recall that the Fréchet spaces of Moscatelli type were introduced and studied by J. Bonet and S. Dierolf in [4]; the general idea behind the construction of such spaces was due to V. B. Moscatelli [7].
Spectral decomposition of spherical immersions with respect to the Jacobi operator
Authors: Arroyo J. , Barros M. , Garay O. J. 
Published: May 2009

AbstractWe study the spectral decomposition with respect to the Jacobi operator, J, of spherical immersions and characterize those with a simple decomposition in terms of the Finite Chen-type submanifolds. As a consequence, we give an application to the inverse problem for J.
Further Integrals Involving E-Functions
Authors: Ragab F. M. 
Published: May 2009

The formulae to be proved arewhere m is a positive integer, p ≧ q + 1, R(mar + k) > 0, r = 1, 2, …, p, and | amp z |ππ. For other values of p and q the result holds if the integral is convergent.
Integrals Involving a Modified Bessel Function of the Second Kind and an E-Function
Authors: Macrobert T. M. 
Published: May 2009

The first formula to be proved iswhere p ≧ q + 1, | amp z | < л, R(k±n + αr)>0, r = l, 2, …, p. For other values of p and q the result is valid if the integral is convergent. A second formula is given in § 3.The following formulae are required in the proof:where R(z);>0, (1);where R(α)>0, | amp z | < л, (2);where the contour starts from -∞ on the ξ-axis, passes round the origin in the positive direction, and ends at -∞ on the ξ-axis, the initial value of amp ζ being - л, (3).
Elliptic Integrals in Terms of Legendre Polynomials
Authors: González M. O. 
Published: May 2009

Consider the elliptic integral of the first kindor, alternatively,where x = sin ϕ. It is customary in the theory of elliptic integrals to let k = sin α, k' = cos α, sot that k'2 + k2 = 1. For convenience we shall also introduce the parameter