bluuebunny/crossref_metadata_2025_split huggingface dataset:
Maximal Quotient Rings of Endomorphism Rings of E(RR)-Torsionfree Generators
Authors: Izawa Tatsuo 
Published: December 2010

Let R be a ring with identity and let H = End (E(RR)) and Q = Dou(E(RR)) = End(HE(RR)). Then Lambek [11] showed that Q is always isomorphic to Qm(R), the maximal right quotient ring of R. And Johnson [10] and Wong-Johnson [26] proved that Qm(R) is regular and right self-injective if and only if R is right non-singular, and then H is isomorphic to Qm(R), too. Moreover, Sandomierski [18] showed that Qm(R) is semi-simple Artinian if and only if R is right finite dimensional and right non-singular. And it is well known that Qm(R) is a quasi-Frobenius ring if and only if E(RR) is a rational extension of RR and the ACC holds on right annihilators of subsets of E(RR).The purpose of this paper is to give some module-theoretic generalizations of these results. Let PR be an E(PR)-torsionless generator, and let S = End(PR), H = End(E(PR)) and Q = Dou(E(PR)).
Diameters of Random Graphs
Authors: Klee Victor , Larman David 
Published: December 2010

For two nodes x and y of a graph G, the distance δG(x,y) is the smallest integer k such that k edges form a path from x to y; δG(x, x) = 0, and δG(x,y) = ∞ when x ≠ y and there is no path from x to y. The diameter δG is the maximum of δG(x, y) as x and y range over the nodes of G. When G is connected, δ(G) is the smallest integer k such that any two nodes of G can be joined by a path formed from at most k edges. When G is not connected, δ(G) = ∞ and there is interest in δc(G), the maximum of δ(G) over the components C of G.For 2 ≧ n < ∞ and 0 ≧ E ≧ n(n − l)/2, let denote the set of all loopless undirected graphs with the node-set {1, …, n} and exactly E edges.
Hypermetric Spaces and the Hamming Cone
Authors: Avis David 
Published: December 2010

We denote by d = (d12, …, d1n, d23, …, dn-1,n) a vector of distances between n points. Such a vector d is called a metric if it satisfies the triangle inequalities(1)The set of all metrics on n points forms a convex polyhedral cone, the extremal properties of which are discussed in [4]. We will be concerned with a sub-cone that is spanned by metrics of the form(2)where t ≧ 0, V is a proper subset of {1, 2, …, n}; and the symbol ⊥ is used for “exclusive or”: i ⊥ j ∈ V means i ∈ V, j ∉ V or i ∉ V,j∉ V.
The Word Problem for Orthogroups
Authors: Gerhard J. A. , Petrich Mario 
Published: December 2010

A semigroup which is a union of groups is said to be completely regular. If in addition the idempotents form a subsemigroup, the semigroup is said to be orthodox and is called an orthogroup. A completely regular semigroup S is provided in a natural way with a unary operation of inverse by letting a-l for a ∈ S be the group inverse of a in the maximal subgroup of S to which a belongs. This unary operation satisfies the identities(1)(2)(3)In fact a completely regular semigroup can be defined as a unary semigroup (a semigroup with an added unary operation) satisfying these identities. An orthogroup can be characterized as a completely regular semigroup satisfying the additional identity(4)
Locally Compact Hjelmslev Planes and Rings
Authors: Lorimer J. W. 
Published: December 2010

Affine and projective Hjelmslev planes are generalizations of ordinary affine and projective planes where two points (lines) may be joined by (may intersect in) more than one line (point). The elements involved in multiple joinings or intersections are neighbours, and the neighbour relations on points respectively lines are equivalence relations whose quotient spaces define an ordinary affine or projective plane called the canonical image of the Hjelmslev plane. An affine or projective Hjelmslev plane is a topological plane (briefly a TH-plane and specifically a TAH-plane respectively a TPH-plane) if its point and line sets are topological spaces so that the joining of non-neighbouring points, the intersection of non-neighbouring lines and (in the affine case) parallelism are continuous maps, and the neighbour relations are closed.In this paper we continue our investigation of such planes initiated by the author in [38] and [39].
Gyclotomic Division Algebras
Authors: Mollin R. A. 
Published: December 2010

Let K be a field of characteristic zero. The Schur subgroup S(K) of Brauer group B(K) consists of those equivalence classes [A] which contain an algebra which is isomorphic to a simple summand of the group algebra KG for some finite group G. It is well known that the classes in S(K) are represented by cyclotomic algebras, (see [16]). However it is not necessarily the case that the division algebra representatives of these classes are themselves cyclotomic. The main result of this paper is to provide necessary and sufficient conditions for the latter to occur when K is any algebraic number field.Next we provide necessary and sufficient conditions for the Schur group of a local field to be induced from the Schur group of an arbitrary subfield. We obtain a corollary from this result which links it to the main result. Finally we link the concept of the stufe of a number field to the existence of certain quaternion division algebras in S(K).
Symbolic Powers of Regular Primes
Authors: Ishibashi Yasunori 
Published: December 2010

In a recent paper [6], P. Seibt has obtained the following result: Let k be a field of characteristic 0, k[T1, … , Tr] the polynomial ring in r indeterminates over k, and let P be a prime ideal of k[T1, … , Tr]. Then a polynomial F belongs to the n-th symbolic power P(n) of P if and only if all higher derivatives of F from the 0-th up to the (n – l)-st order belong to P.In this work we shall naturally generalize this result so as to be valid for primes of the polynomial ring over a perfect field k. Actually, we shall get a generalization as a corollary to a theorem which asserts: For regular primes P in a k-algebra R of finite type, a certain differential filtration of R associated with P coincides with the symbolic power filtration (P(n))n≧0.
Necessary Conditions for Universal
Interpolation in
Authors: Squires W. A. 
Published: December 2010

Let be the space of Fourier transforms of distributions with compact support, or equivalently, the space of entire functions h satisfying the growth condition(1)where p(z) = |Imz| + log (1 + |z|2) and A, B are constants depending only on h. A sequence with |zk| ↑ ∞ is said to be a universal interpolation sequence for if for all such that(2)for constants A, B independent of k, there exists such that f(zk) = ak. In this note we will consider necessary conditions for universal interpolation in and more general subspaces of the entire functions.
Stability and Categoricity of Lattices
Authors: Smith Kenneth W. 
Published: December 2010

This paper is a contribution to applied stability theory. Our purpose is to investigate the complexity of lattices by determining the stability of their first order theories.Stability measures the complexity of a theory T by counting the number of different “kinds” of elements in models of T. The notion of ω-stability was introduced by Morley [26] in 1965 and generalized by Shelah [31] in 1969. Shelah classified all first order theories according to their stability properties.Stability and -categoricity are closely related (see [26] and [1]). In fact, the notions of stable, superstable and ω-stable can be regarded as successive approximations of -categorical. -categoricity is a very strong property while stability, superstability and ω-stability facilitate the classification of more “complex” theories.
Modeles Bifiltres: Une Plaque Tournante en Homotopie Rationnelle
Authors: Felix Yves 
Published: December 2010

A chaque c.w. complexe X, 1-connexe, de type fini, est associé une
algèbre différentielle graduée commutative (ΛZ, d) qui est un modèle dans le sens de Sullivan [10] et représente donc le type d'homotopie rationnelle de X.ΛZ est munie d'une seconde graduation Z = ⊕q≧0Zq. La différentielle d se décompose alors sous la forme et d0(Zp) ⊂ (Λ2Z)p–1 et di(Zp) ⊂ Zp–i, i ≧ 1. En particulier d0 est purement quadratique tandis que di est du premier degré, i ≧ 1.L'algèbre ΛZ et la partie quadratique d0 ne dépendent que des nombres de Betti de X. Les différents types d'homotopie rationnelle de nombres de Betti donnés sont donc paramétrés par les déformations di. La partie d1 exprime la structure multiplicative de l'algèbre de cohomologie rationnelle de X, les parties d2, d3, d4. … les structures algébriques plus complexes du type d'homotopie rationnelle.
Krull Semigroups and Divisor Class Groups
Authors: Chouinard II Leo G. 
Published: December 2010

R. Matsuda has shown that a group ring is a Krull domain if and only if the coefficient ring is a Krull domain and the group is a torsion-free abelian group satisfying the ascending chain condition (ace) on cyclic subgroups [6]. D. F. Anderson has used this to obtain a partial determination of when a semigroup ring is a Krull domain, and under certain circumstances to describe the divisor class group of such a ring ([1], [2]). Using some of Anderson's techniques, but taking a different approach, we arrive at a complete answer of a different nature to these questions. We call a semigroup satisfying the major new conditions arising a Krull semigroup, and define its divisor class group.In particular, every abelian group is the divisor class group of such a ring, and it follows that every abelian group is the divisor class group of a quasi-local ring, which seems to be a new result.
On the Homotopy Property of Nussbaum's Fixed Point Index
Authors: Fournier Gilles , Fournier Reine 
Published: December 2010

In [14] R. D. Nussbaum generalized the fixed point index to a class of maps larger than the one in [5]. Unfortunately his homotopy property conditions are more restrictive than the often more readily verifiable ones of Eells-Fournier. In this paper we shall try to find an intermediate class of maps which will contain all the known examples of maps for which the index is defined and for which the condition of Eells-Fournier will imply the homotopy property.In doing so, we shall give general conditions for which the sum of a compact map and a differentiable map will be a map having a fixed point index and for which the Lefschetz fixed point theorem is true.
Simple Links in Locally Compact Connected Hausdorff Spaces are Nondegenerate
Authors: John David 
Published: December 2010

The fact that simple links in locally compact connected metric spaces are nondegenerate was probably first established by C. Kuratowski and G. T. Whyburn in [2], where it is proved for Peano continua. J. L. Kelley in [3] established it for arbitrary metric continua, and A. D. Wallace extended the theorem to Hausdorff continua in [4]. In [1], B. Lehman proved this theorem for locally compact, locally connected Hausdorff spaces. We will show that the locally connected property is not necessary.A continuum is a compact connected Hausdorff space. For any two points a and b of a connected space M, E(a, b) denotes the set of all points of M which separate a from b in M. The interval ab of M is the set E(a, b) ∪ {a, b}.
Primitive Generators for Algebras
Authors: Kochman Stanley O. 
Published: December 2010

LetHbe a graded commutative algebra with a nice set of algebra generators. LetHalso be a comodule over a Hopf algebraA. In Section 2 we give conditions under which certain of these generators ofHcan be rechosen to be primitive. In addition we give explicit formulas expressing these primitive generators in terms of the original set of generators.In Section 3 we apply the theory of Section 2 to the modphomology of the Thorn spectraMO, MUandMSp.In particular we give two explicit descriptions of the image of the Hurewicz homomorphism forMO.One of these makes explicit the recursive computation of E. Brown and F. Peterson [1].In Section 4 we give a variation of the theory of Section 2 which computes primitive generators of certain Hopf algebras. This theory is applied to study the primitive elements ofH*(BU)andH*(SO;Z2).
Additivity of the Pn-Integral (2)
Authors: Cross G. E. 
Published: December 2010

The problem of additivity of the Pn-integral on abutting intervals was considered in [2] and in [5]. It was noted in [2] that the necessary and sufficient conditions for additivity for the P2-integral obtained by Skvorcov in [5] could be completely generalized to the Pn-integral, n > 2, if a key lemma (corresponding to Skvorcov's Lemma 3 [6]) could be proved. We provide a proof of that lemma in this paper and hence obtain the general additivity result.The definitions and notation of [2] are used in the following, except that we shall take the following as the definition of Pn-major and minor functions:Definition 1.1. Let f(x) be a function defined in [a, b] and let a1, i = 1, 2, …, n, be fixed points such that a = a1 < a2 < … < an = b.
The Application of Lagrangian Methods to the Enumeration of Labelled Trees with Respect to Edge Partition
Authors: Goulden I. P. , Jackson D. M. 
Published: December 2010

In an earlier paper [6] we considered the application of Lagrangian methods to the enumeration of plane rooted trees with given colour partition. We obtained an expression which generalised Tutte’s result [9], and a correspondence, which, when specialised, gives the de Bruijn-van Aardenne Ehrenfest-Smith-Tutte Theorem [1]. A corollary of these results is a one-to-one correspondence [4], between trees and generalised derangements, for which no combinatorial description has yet been found.In this paper we extend these methods to the enumeration of rooted labelled trees to demonstrate how another pair of well-known and apparently unrelated theorems may be obtained as the result of a single enumerative approach. In particular, we show that a generalisation of Good's result [3], also considered by Knuth [7], and the matrix tree theorem [8] have a common origin in a single system of functional equations, and that they correspond to different coefficients in the power series solution.
Bounds on Betti Numbers
Authors: Ramras Mark 
Published: December 2010

The Betti numbers βn(k) of the residue class field k = R/m of a commutative local ring (R, m) have been studied for about 20 years, primarily as the coefficients of the Poincaré series of E . Several authors have obtained results about the growth of the sequence {βn(k)}.For example, Gulliksen [3] showed that when R is non-regular, the sequence is non-decreasing. More recently, Avramov [1] studied asymptotic properties of {βn(k)} and found that under certain conditions the growth is exponential, i.e., there is a natural number p such that for all n, βpn(k) ≧ 2n.In this paper, we examine the sequence {βn(M)} for arbitrary finitely generated non-free modules M over any commutative local artin ring R. We establish the following bounds:123where l(X) is the length of X.
Resolution D'Equations Associees a un Systeme de Tchebycheff
Authors: Dubuc Serge , Savoie Jean 
Published: December 2010

Soit {f1(x),f2(x), …,fm(x)} un système de Tchebycheff de dimension m, c'est-à-dire les fonctions fj(x) sont des fonctions réelles continues définies sur un intervalle ouvert (a, b) et toute fonction de la forme admet au plus m — 1 racines dans (a, b) lorsqu'au moins un des coefficients Cj diffère de 0. Notre point de départ est un théorème dû à Krein [3]. On se limite au cas où la dimension m est paire, m = 2n. Ce théorème dit que la totalité Ω des points de R2n qui se représentent ainsi sont n points distincts de (a, b) et où pi > 0, 1 ≦ i≦n, forme effectivement un ouvert convexe de R2n. Les systèmes d'équations que nous voulons traiter sont justement les équations:I
A Stickelberger Condition on Cyclic Galois Extensions
Authors: Childs L. N. 
Published: December 2010

LetRbe a commutative ring,Ca finite abelian group,Sa Galois extension ofRwith groupC, in the sense of [1]. ViewingSas anRC-module defines the Picard invariant map [4] from the Harrison group Gal (R,C) of isomorphism classes of Galois extensions ofRwith groupCto CI (RC), the class group ofRC. The image of the Picard invariant map is known to be contained in the subgrouphCl (RC) of primitive elements of CI (RC) (for definition see below). Characterizing the image of the Picard invariant map has been of some interest, for the image describes the extent of failure of Galois extensions to have normal bases.LetRbe the ring of integers of an algebraic number fieldK.
Semi-Prime Rings Whose Homomorphic Images are Serial
Authors: Levy Lawrence S. , Smith Patrick F. 
Published: December 2010

A theorem of Eisenbud, Griffith, and Robson states that if R is hereditary and noetherian (on both the left and right) then every proper homomorphic image of R is a generalized unserial ring (see, for example, [3, p. 244]). Singh [11, p. 883] states a converse: If R is a right bounded, noetherian prime ring, all of whose proper homomorphic images are generalized uniserial rings, then (every divisible right R-module is injective, so) R is right hereditary. (Actually, Singh omitted the clearly necessary “bounded” condition.) Singh's theorem generalizes results of [9, Proposition 15], [2, Theorem 2.1], and [8], about commutative rings.We will call a semi-prime ring R essentially right bounded if each essential right ideal contains a two-sided ideal which is essential as a right ideal. In case R is prime, “essentially right bounded” coincides with “right bounded”.
Perfect Sets of Uniqueness on the Group 2ω
Authors: Yoneda Kaoru 
Published: December 2010

Let ω0, ω1, … denote the Walsh-Paley functions and let G denote the dyadic group introduced by Fine [3]. Recall that a subset E of G is said to be a set of uniqueness if the zero series is the only Walsh series ∑ akωk which satisfiesA subset E of G which is not a set of uniqueness is called a set of multiplicity.It is known that any subset of G of positive Haar measure is a set of multiplicity [5] and that any countable subset of G is a set of uniqueness [2]. As far as uncountable subsets of Haar measure zero are concerned, both possibilities present themselves. Indeed, among perfect subsets of G of Haar measure zero there are sets of multiplicity [1] and there are sets of uniqueness [5].
Isometries of Weighted Bergman Spaces
Authors: Kolaski Clinton J. 
Published: December 2010

In [2], [8] and [10], Forelli, Rudin and Schneider described the isometries of the Hp spaces over balls and polydiscs. Koranyi and Vagi [6] noted that their methods could be used to describe the isometries of the Hp spaces over bounded symmetric domains. Recently Kolaski [4] observed that the algebraic techniques used above and Rudin's theorem on equimeasurability extended to the Bergman spaces over bounded Runge domains. In this paper we use the same general argument to characterize the onto linear isometries of the weighted Bergman spaces over balls and polydiscs, (all isometries referred to are assumed to be linear).2. Preliminaries. Horowitz [3] first defined the weighted Bergman space Ap,α(0 < p < ∞, 0 < α < ∞) to be the space of holomorphic functions f in the disc which satisfy(1)
On an Inequality of S. Bernstein
Authors: Frappier C. , Rahman Q. I. 
Published: December 2010

Let R > 1 and denote by ℰR the ellipse(1)If Pn is a polynomial of degree at most n such that(2)then ([2]; also see [13, p. 337] and [9, p. 158, Prob. No. 270])(3)The standard proof of this well known result runs as follows. The function(4)is entire and in view of (2) we haveHence by the maximum modulus principle(5)which is clearly equivalent to (3).
Symbole Holomorphe
Authors: Meril A. 
Published: December 2010

Soit T un endomorphisme continu de , nous montrons qu'il existe une fonction entière S sur Cn × Cn telle que ζ → S(x, ζ) soit de type exponential sur Cn avec croissance controlée uniformément lorsque x parcourt un compact de Cn, de telle sorte que pour on ait( désigne la transformée de Fourier-Borel d'une fonctionnelle analytique). Une telle fonction S sera dite un symbole holomorphe sur Cn. Réciproquement nous montrons que si S est une fonctionnelle analytique, la formule précédente permet de définir un endomorphisme continu (encore noté S) de .
Brauer Groups, Class Groups and Maximal Orders for a Krull Scheme
Authors: Lee Heisook , Orzech Morris 
Published: December 2010

In a previous paper [13] one of us considered Brauer groups Br(C) and class groups Cl(C) attached to certain monoidal categories C of divisorial R-lattices. That paper showed that the groups arising for a suitable pair of categories C1 ⊆ C2 could be related by a tidy exact sequenceIt was shown that this exact sequence specializes to a number of exact sequences which had formerly been handled separately. At the same time the conventional setting of noetherian normal domains was replaced by that of Krull domains, thus generalizing previous results while also simplifying the proofs. This work was carried out in an affine setting, and one aim of the present paper is to carry these results over to Krull schemes. This will enable us to recover the non-affine version of an exact sequence obtained by Auslander [1, p. 261], as well as to introduce a new, non-affine version of a different sequence derived by the same author [2, Theorem 1].
Coefficients in Expansions of Certain Rational Functions
Authors: Evans Ronald , Ismail Mourad E. H. , Stanton Dennis 
Published: December 2010

The constant term of certain rational functions has attracted much attention recently. For example the Dyson conjecture; that the constant term ofis the multinomial coefficienthas spawned many generalizations (see [2], [7]). In this paper we consider some other families of rational functions which have interesting constant terms. For example, Corollary 4 states that the constant term of(1.1)is . Here, and throughout this paper, A and B denote fixed positive integers.In order to prove this result, we consider the rational function in two variables
Systemes Fondamentaux D'unites de Certains Corps de Degre 4 et de Degre 8 Sur Q
Authors: Levesque Claude 
Published: December 2010

Lorsque Kn = Q(ω) est une extension algébrique de degré n sur Q telle queavec D ∈ N, d ∈ Z, d|D2 et D2 + 4d > 0, nous avons prouvé [1] en utilisant certaines idées de Halter-Koch et Stender [2] que sialorsest un système indépendant d'unités de Kn.
Solvable and Nilpotent Subgroups of GL(n,qm)
Authors: Wolf Thomas R. 
Published: December 2010

Let V ≠ 0 be a vector space of dimension n over a finite field of order qm for a prime q. Of course, GL(n, qm) denotes the group of -linear transformations of V. With few exceptions, GL(n, qm) is non-solvable. How large can a solvable subgroup of GL(n, qm) be? The order of a Sylow-q-subgroup Q of GL(n, qm) is easily computed. But Q cannot act irreducibly nor completely reducibly on V.Suppose that G is a solvable, completely reducible subgroup of GL(n, qm). Huppert ([9], Satz 13, Satz 14) bounds the order of a Sylow-q-subgroup of G, and Dixon ([5], Corollary 1) improves Huppert's bound. Here, we show that |G| ≦ q3nm = |V|3. In fact, we show thatwhere
Group Rings with Units of Bounded Exponent over the Center
Authors: Coelho Sônia P. 
Published: December 2010

Let KG be the group ring of a group G over a field K, and U its group of units. Given a group H, we shall denote by ξ(H) the center of H and by T(H) the set of all its torsion elements.The following question appears in [5, p. 231]: When is Un ⊂ ξ (U), for some n? It was considered by G. Cliff and S. K. Sehgal in [1], where G is assumed to be a solvable group. A complete answer at characteristic zero is given there. Also they obtain partial results at characteristic p ≠ 0, with certain restrictions on the exponent n.