bluuebunny/crossref_metadata_2025_split huggingface dataset:
Semigroup Compactifications of Direct and Semidirect Products
Authors: Milnes Paul 
Published: December 2010

AbstractA classical result of I. Glicksberg and K. de Leeuw asserts that the almost periodic compactification of a direct product S × T of abelian semigroups with identity is (canonically isomorphic to) the direct product of the almost periodic compactiflcations of S and T. Some efforts have been made to generalize this result and recently H. D. Junghenn and B. T. Lerner have proved a theorem giving necessary and sufficient conditions for an F-compactification of a semidirect product S⊗σT to be a semidirect product of compactiflcations of S and T. A different such theorem is presented here along with a number of corollaries and examples which illustrate its scope and limitations. Some behaviour that can occur for semidirect products, but not for direct products, is exposed
FPF Rings and Some Conjectures of C. Faith
Authors: Page S. S. 
Published: December 2010

AbstractA left FPF ring is a ring R such that every finitely generated faithful left R -module generates the category of left R-modules. It is shown that such rings split into R = A⊕B, where A is a two sided ideal, and A contains the left singular ideal of R as an essential submodule. If R is FPF on both sides B is two sided too, and R is the product of A and B. An example shows this is the best possible and that right FPF does not imply left FPF.
Inclusion Theorems for the Absolute Summability of Divergent Integrals
Authors: Diamond Harvey , Kuttner Brian , Raphael Louise A. 
Published: December 2010

AbstractSome inclusion theorems are obtained relating the absolute summability of divergent integrals of the form under three summability methods: Abelian A(x), Abelian A(lnx) and Stieltjes S(x).
Curvature of Level Curves of Harmonic Functions
Authors: Ortel Marvin , Schneider Walter 
Published: December 2010

AbstractIf H is an arbitrary harmonic function defined on an open set Ω⊂ℂ, then the curvature of the level curves of H can be strictly maximal or strictly minimal at a point of Ω. However, if Ω is a doubly connected domain bounded by analytic convex Jordan curves, and if H is harmonic measure of Ω with respect to the outer boundary of Ω, then the minimal curvature of the level curves of H is attained on the boundary of Ω.
Nearnesses and T0-Extensions of Topological Spaces
Authors: Dean Alice M. 
Published: December 2010

AbstractIn [3], Reed establishes a bijection between the (equivalence classes of) principal T1-extensions of a topological space X and the compatible, cluster-generated, Lodato nearnesses on X. We extend Reed's result to the T0 case by obtaining a one-to-one correspondence between the principal T0-extensions of a space X and the collections of sets (called “t-grill sets”) which generate a certain class of nearnesses which we call “t-bunch generated” nearnesses. This correspondence specializes to principal T0-compactifications. Finally, we show that there is a bijection between these t-grill sets and the filter systems of Thron [5], and that the corresponding extensions are equivalent.
Metrizability Conditions for Completely Distributive Lattices
Authors: Gierz G. , Lawson J. D. , Stralka A. R. 
Published: December 2010

AbstractA lattice is said to be essentially metrizable if it is an essential extension of a countable lattice. The main result of this paper is that for a completely distributive lattice the following conditions are equivalent: (1) the interval topology on L is metrizable, (2) L is essentially metrizable, (3) L has a doubly ordergenerating sublattice, (4) L is an essential extension of a countable chain.
Lie Ideals in Associative Algebras
Authors: Murphy G. J. 
Published: December 2010

AbstractIt is shown that in a certain extensive class of algebras one can associate with each Lie ideal a corresponding associative ideal which facilitates the study of Lie ideals, especially for simple algebras. We apply this construction to obtain new, simpler proofs of some known results of Herstein [10] and others on the Lie structure of associative rings.
Characterizations of *-Multiplication Domains
Authors: Houston Evan G. , Malik Saroj B. , Mott Joe L. 
Published: December 2010

AbstractLet * be a finite-type star-operation on an integral domain D. If D is integrally closed, then D is a *-multiplication domain (the *-finite *-ideals form a group) if and only if each upper to 0 in D[x] contains an element f with c(f)* = D. A finite-type star operation on D[x] naturally induces a finite-type star operation on D, and, if each *-prime ideal P of D[x] satisfies P ∩ D = 0 or P = (P ∩ D)D[x], then D[x] is a *-multiplication domain if and only if D is.
On Fundamental Approximative Absolute Neighborhood Retracts
Authors: Sanjurjo J. M. R. 
Published: December 2010

AbstractIn this paper we define and study a class of compacta under the name of Fundamental Approximative Absolute Neighborhood Retracts. This class includes Borsuk’s Fundamental Absolute Neighborhood Retracts and Approximative Absolute Neighborhood Retracts in the sense of M. H. Clapp as proper subclasses. We also introduce the notion of q-strong movability and prove that Fundamental Approximative Absolute Neighborhood Retracts coincide with q-strongly movable compacta.
Von Neumann Operators in
Authors: Seddighi Karim 
Published: December 2010

AbstractFor a connected open subset Ω of the plane and n a positive integer, let be the space introduced by Cowen and Douglas in their paper, “Complex geometry and operator theory”. Our main concern is the case n = 1, in which case we show the existence of a functional calculus for von Neumann operators in for which a spectral mapping theorem holds. In particular we prove that if the spectrum of , is a spectral set for T, and if , then σ(f(T)) = f(Ω)- for every bounded analytic function f on the interior of L, where L is compact, σ(T) ⊂ L, the interior of L is simply connected and L is minimal with respect to these properties. This functional calculus turns out to be nice in the sense that the general study of von Neumann operators in is reduced to the special situation where Ω is an open connected subset of the unit disc with .
A Note on Partition-Inducing Automorphism Groups
Authors: Pettet Martin R. 
Published: December 2010

AbstractWe consider a finite group G with a group A acting on it in such a way as to induce a partition of G# (a situation which arises in the study of centralizer near-rings). With the additional hypothesis that (|Aω|, |G|) = 1, it is shown that either A is semiregular on G# or G is an irreducible module for A.
Semicritical Rings and the Quotient Problem
Authors: Kosler Karl A. 
Published: December 2010

AbstractThe purpose of this paper is to examine the relationship between the quotient problem for right noetherian nonsingular rings and the quotient problem for semicritical rings. It is shown that a right noetherian nonsingular ring R has an artinian classical quotient ring iff certain semicritical factor rings R/Ki, i = 1,…,n, possess artinian classical quotient rings and regular elements in R/Ki lift to regular elements of R for all i. If R is a two sided noetherian nonsingular ring, then the existence of an artinian classical quotient ring is equivalent to each R/Ki possessing an artinian classical quotient ring and the right Krull primes of R consisting of minimal prime ideals. If R is also weakly right ideal invariant, then the former condition is redundant. Necessary and sufficient conditions are found for a nonsingular semicritical ring to have an artinian classical quotient ring.
Factorized Groups with max, min and min-p
Authors: Amberg Bernhard 
Published: December 2010

AbstractLet be a class of groups which is closed under the forming of subgroups, epimorphic images and extensions. It is shown that every soluble product G = AB of two -subgroups A and B, one of which satisfies max or min, is an -group (Theorem A). If X satisfies an additional requirement, then every soluble product G = AB of two -subgroups A and B, one of which is a torsion group with min-p for every prime p, is an -group (Theorem B). Corollary: Every soluble product G = AB of two π-subgroups A and B with min-p for every prime p in the set of primes π, is a π -group with min-p for every p.
A Measure for Polynomials in Several Variables
Authors: Myerson Gerald 
Published: December 2010

AbstractWe define a notion of measure for polynomials in several variables, basing our construction on the geometry of the zero-set of the polynomial. For polynomials in one variable, this measure reduces to the usual one. We begin the development of the theory of this measure along lines parallel to the theory of Mahler’s measure, indicating the differences and similarities between the two.Let P be a polynomial in one variable with complex coefficients, P(z) = a0Π(z - αj). The measure of P, denoted M(P), is defined by1As is well-known, an application of Jensen’s formula yields2
On an Oval with the Four Point Pascalian Property
Authors: Fernandes Olga 
Published: December 2010

AbstractIn this paper it is proved that a finite translation plane of order n ≡ 3 (mod 4) which contains an oval with the four point Pascalian property, or a finite dual translation plane of order n ≡ 3 (mod 4) which contains an oval with the four point Pascalian property, can be coordinatized by a commutative semifield.
Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
Authors: Gonçalves Jairo Z. 
Published: December 2010

AbstractLet KG be the group ring of the group G over the field K and U(KG) its unit group. When G is finite we derive conditions which imply that every noncentral subnormal subgroup of U(KG) contains a free group of rank two. We also show that residual nilpotence of U(KG) coincides with nilpotence, this being no longer true if G is infinite.We can answer partially the following question: when is G sub-normal in U(KG)?
Commutative Systems of Covariance and a Generalization of Mackey's Imprimitivity Theorem
Authors: Ali S. Twareque 
Published: December 2010

AbstractTwo results are obtained in this paper. The first is a generalization of the imprimitivity theorem of Mackey, when the associated projection-valued measure is replaced by a commutative positive operator valued measure. The second is a necessary and sufficient condition for such a system of covariance to possess an overcomplete, covariant family of coherent states.
Onp-Large Subgroups ofp-Torsion Groups
Authors: Benabdallah K. , Yoshioka S. 
Published: December 2010

ResuméLes groupesp-torsion forment une classe de groupes abéliens mixtes dont les sous-groupes dep-base sont de torsion. Nous montrons ici que la généralisation naturelle à ces groupes de la notion de sous-groupe large développée pour les groupes primaires par R. S. Pierce, permet d'obtenir des résultats analogues. Ainsi nous caractérisons les sous-groupesp-larges d'un groupep-torsionGen fonction des suites non-décroissantes d'entiers non-négatifsu= (ui) qui satisfont à la condition d'écart pourG. On obtient: un sous-groupe A du groupep-torsionGestp-large si, et seulement si A est de la formeG(u) pour une suiteutelle que pour toutx ∈ G, la suite (h(pix)) est plus grande presque partout que la suiteu.Nous déterminons aussi, les sous-groupesp-large de, le complétép-adique d'une somme directe de groupes cycliques non bornésB, ainsi que ceux des sous-groupesp-purs totalement invariants deengendrés par un élément.
Locally Uniformly Rotund Renorming and Injections Into c0(Γ)
Authors: Godefroy G. , Troyanski S. , Whitfield J. , Zizler V. 
Published: December 2010

AbstractA norm |⋅| on a Banach space X is locally uniformly rotund (LUR) if lim |xn — x| = 0 for every xn, x ∈ X for which lim2|x|2 + 2 |xn|2-|xn+xn|2 = 0. It is shown that a Banach space X admits an equivalent LUR norm provided there is a bounded linear operator T of X into c0(Γ) such that T* c*0(Γ) is norm dense in X*. This is the case e.g. if X* is weakly compactly generated (WCG).
On a Result of Smith and Subbarao Concerning a Divisor Problem
Authors: Nowak Werner Georg 
Published: December 2010

AbstractLet d(n;l,k) denote the number of divisors of the positive integer n which are congruent to I modulo k. The objective of the present paper is to prove that (for some exponent θ<⅓)holds uniformly in l, k and x satisfying 1≤l≤k≤x. This improves a recent result due to R. A. Smith and M. V. Subbarao [3].
Two Inequalities for Planar Convex Sets
Authors: Tsintsifas George 
Published: December 2010

AbstractB. Grünbaum, J. N. Lillington and lately R. J. Gardner, S. Kwapien and D. P. Laurie have considered inequalities defined by three concurrent straight lines in the interior of a planar compact convex set. In this note we prove two elegant conjectures by R. J. Gardner, S. Kwapien and D. P. Laurie.
Finite Intersections of Pid or Factorial Overrings
Authors: Anderson D. D. , Anderson David F. 
Published: December 2010

AbstractIn this paper we study when an integral domain is a finite intersection of PID or factorial overrings. We show that any Krull domain is the intersection of a PID and a field. We give several sufficient conditions for a Krull domain to be an intersection of two PID or factorial overrings.
Structure of Certain Periodic Rings
Authors: Abu-Khuzam Hazar , Yaqub Adil 
Published: December 2010

AbstractLet R be a periodic ring, N the set of nilpotents, and D the set of right zero divisors of R. Suppose that (i) N is commutative, and (ii) every x in R can be uniquely written in the form x = e + a, where e2 = e and a ∊ N. Then N is an ideal in R and R/N is a Boolean ring. If (i) is satisfied but (ii) is now assumed to hold merely for those elements x ∊ D, and if 1 ∊ R, then N is still an ideal in R and R/N is a subdirect sum of fields. It is further shown that if (i) is satisfied but (ii) is replaced by: "every right zero divisor is either nilpotent or idempotent," and if 1 ∊ R, then N is still an ideal in R and R/N is either a Boolean ring or a field.
Connected Maps and Essentially Connected Spaces
Authors: Nishiura Eizo 
Published: December 2010

AbstractThe paper discusses some consequences of weak monotonicity for connected maps in relation to essential connectedness of a space. The first main result gives conditions under which the image by a connected map of an essentially connected space is essentially connected. The second is that, for a connected mapping of a connected, 1 .c. space to a WLOTS-wise and essentially connected space, w-monotonicity implies monotonicity. The remainder of the paper discusses continuity properties of connected, w-monotone mappings with WLOTS-wise and essentially connected range.
Stiefel-Whitney Classes of a Symmetric Bilinear Form — A Formula of Serre
Authors: Snaith Victor 
Published: December 2010

AbstractLet K be a field of characteristic different from two. Let L be a finite separable extension of K. If is the separable closure of K, we have a continuous homomorphism π : Ga(/K) → ∑n(n - [L : K]). We give a very short proof of Serre's formula which evaluates the Hasse-Witt invariant of a symmetric bilinear form, transferred from L, in terms of the topological Stiefel-Whitney classes of IT.
The Chowla-Selberg Method for Fourier Expansion of Higher Rank Eisenstein Series
Authors: Terras Audrey 
Published: December 2010

AbstractThe terms of maximal rank in Fourier expansions of Eisenstein series for GL(n, ℤ) are obtained by an analogue of a method of Chowla and Selberg. The coefficients involve matrix analogues of divisor functions as well as K-Bessel functions for GL(n). The discussion involves a few properties of Hecke operators.
Small Solutions of Congruences in a Large Number of Variables
Authors: Schmidt Wolfgang M. 
Published: December 2010

AbstractIt is shown that a system of congruences 1(x) ≡ . . . ≡ (x) = 0 (mod m)where each i(x) = i,(x1, .. . ,x2,) is a form of degree at most k has a nontrivial solution x satisfying |xi|≦cm(½)+∊ (i=1,...,S)with c = c(k,r,∊), provided that ∊ > 0 and that S > S1(k,r,∊).
Numbers Differing from Consecutive Squares by Squares
Authors: Barbeau E. J. 
Published: December 2010

AbstractIt is shown that there are infinitely many natural numbers which differ from the next four greater perfect squares by a perfect square. This follows from the determination of certain families of solutions to the diophantine equation 2(b2 + 1) = a2 + c2. However, it is essentially known that any natural number with this property cannot be 1 less than a perfect square. The question whether there exists a number differing from the next five greater squares by squares is open.
Convergence and Analytic Continuation for a Class of Regular C-Fractions
Authors: Masson D. 
Published: December 2010

AbstractRegular C-fractions f(α) = 1 + a1α/1 + a2α/1 + . .. with an = an2 + bn + c + Vn, |Vn| sufficiently small are examined. In the case Vn = 0, exact expressions are obtained which reveal a two sheeted Riemann structure for f(α). If Vn ≠ 0 analytic properties are obtained by means of perturbation theory applied to the associated difference equation. A conjecture that f(α) is the ratio of two entire functions of for an even larger class of C-fractions is proved for the case .
M-Ideals in L(l1, E)
Authors: Fleming D. J. , Giarrusso D. M. 
Published: December 2010

AbstractIn this article it is shown that for any Banach space E,L (l1,E) always contains uncountably many distinct A/-ideals that are closed subspaces of K(l1,E) and which are not complemented in L (l1,E) . Using standard duality arguments one obtains the result that infinitely many distinct subspaces of K(E, c0) are M-ideals in L(E, c0). In particular, for the case E = c0, this shows that the uniqueness conditions enjoyed by K(lp), p > 1, is not valid for E = c0. The results are obtained by utilizing the identification of L (l1,E) with the vector-valued sequence space lx(E) and to exploit natural decompositions of lx(E)’ afforded by a class of Lprojections on lx(E)’ induced by certain E'-valued vector measures.
Products and Cardinal Invariants of Minimal Topological Groups
Authors: Douglass L. Grant  , W. W. Comfort  
Published: December 2010

AbstractIt is a question of Arhangel'skiĭ [1] (Problem 2) whether the identity ψ(G) = X(G) holds for every minimal Hausdorff topological group G = 〈G,u〉). (Here, as usual, ψ(G), the pseudocharacter of G, is the least cardinal number K for which there is such that and and x(G), the character of G,is the least cardinality of a local base at e for (〈G,u〉.) That 〈G, u〉 is minimal means that, if v is a Hausdorff topological group topology for G and v ⊂ u, then v = u.In this paper, we give some conditions on G sufficient to ensure a positive response to Arhangel'skiï's question, and we offer an example which responds negatively to a question on minimal groups posed some years ago (cf. [6] (p. 107) and [4] (p. 259)).
Functors on Finite Vector Spaces and Units in Abelian Group Rings
Authors: Hoechsmann Klaus 
Published: December 2010

AbstractIf A is an elementary abelian group, let (A) denote the group of units, modulo torsion, of the group ring Z[A]. We study (A) by means of the compositewhere C and B run over all cyclic subgroups and factor-groups, respectively. This map, γ, is known to be injective; its index, too, is known. In this paper, we determine the rank of γ tensored (over Z);with various fields. Our main result depends only on the functoriality of
A Note on Permutations and Topological Entropy of Continuous Maps of the Interval
Authors: Byers Bill 
Published: December 2010

AbstractSuppose f is a continuous endomorphism of an interval which has a periodic orbit, p0 < P1 < … < pn, that defines a permutation a by f(pi) = pσ(i). If σ is irreducible the topological entropy of f is bounded below by the logarithm of the spectral radius of an n x n matrix which is induced by σ.
A Problem on Relative Projectivity for Abelian Groups
Authors: Feigelstock S. , Raphael R. 
Published: December 2010

AbstractThe article studies the class of abelian groups G such that in every direct sum decomposition G = A ⊕ B, A is 5-projective. Such groups are called pds groups and they properly include the quasi-projective groups.The pds torsion groups are fully determined.The torsion-free case depends on a lemma that establishes freedom in the non-indecomposable case for several classes of groups. There is evidence suggesting freedom in the general reduced torsion-free case but this is not established and prompts a logical discussion. It is shown, for example, that pds torsion-free groups must be Whitehead if they are not indecomposable, but that there exists Whitehead groups that are not pds if there exist non-free Whitehead groups.The mixed case is characterized and examples are given.
Finite Regular Covers of Surfaces
Authors: Cusick Larry W. 
Published: December 2010

AbstractLet Tk = T1#...#T1 T1 = Sl x Sl, Uk = ℝP2#... #ℝP2, and G is a finite group. We prove (1) Every free action of G on Ul + 2 lifts to a free action of G on the orientable two fold cover Tl+1 → Ul+1 and (2) The minimum k such that can act freely on Tk is ml((l - 2)/2) + 1 if m = 2 or l is even and ml((l - 1)/2) + 1 otherwise.
The Relation Between Stable Operations for Connective and Non-Connective p-Local Complex K-Theory
Authors: Johnson Keith 
Published: December 2010

AbstractThe question of which degree 0 stable cohomology operations for connective K-theory localized at a prime p arise from operations for non-connective K-theory is investigated. A necessary and sufficient condition is established, and an example of a connective operation not arising in this way is constructed.
The Long Annulus Theorem
Authors: Evans Benny 
Published: December 2010

AbstractGiven a properly embedded incompressible surface F in a Haken manifold M, there is an integer n depending only on M and F with the following property: If there is a singular annulus in M that meets F in more then n nontrivial loops that are not freely homotopic on F then M contains an essential torus or annulus, or M is a bundle with fiber F, or M is a doubled twisted I-bundle with doubling surface F.
A Practical Two-Dimensional Ergodic Theorem
Authors: Scarowsky Manny , Boyarsky Abraham 
Published: December 2010

AbstractLet τ:[0, 1] → [0, 1] be defined by τ(x) = 2x on [0, 1/2,] and τ(JC) = 2(1 - x) on [5, 1], and let T:[0, 1] x [0, 1] → [0, 1] x [0, 1] be defined by T(x,y) = (τ(x), τ(y))- Letwhere p is a prime > 2, and a and M are integers. Consider T restricted to θM x θN, 1 < M < N. Let X = ((2a)/(pM), (2b)/(pN)) ∈ θM x θN and let per(X) denote the length of the period of X.Then,where m is Lebesque measure on [0, 1], and C is independent of p, N, M, a and b. Thus, as p → or as N - M and M→ →,
Remarks on Entire Functions of Exponential Type
Authors: Frappier Clément 
Published: December 2010

AbstractA classical result of Laguerre says that if P is a polynomial of degree n such that P(z) ≠ 0 for | z | < 1 then (ξ - z)P' (z) + nP(z) ≠ 0 for | z | < 1 and | ξ | < 1. Rahman and Schmeisser have obtained an extension of that result to entire functions of exponential type: if f is an entire function of exponential type τ, bounded on ℝ, such that hf(π/2) = 0 then (ξ- l)f'(z) + iτ(z) ≠ 0 for Im(z) > 0 and | ξ | < 1, whenever f(z) ≠ 0 if Im(z) > 0. We obtain a new proof of that result. We also obtain a generalization, to entire functions of exponential type, of a result of Szegö according to which the inequality | P(Rz) — P(z) | < Rn - 1, | z | ≤ 1, R ≥ 1, holds for all polynomials P, of degree ≤ n, such that | P(z) | ≤ 1 for | z | ≤ 1.
A Result on Derivations with Algebraic Values
Authors: Di Vincenzo Onofrio M. 
Published: December 2010

AbstractLet R be a prime algebra over a field F and let d be a non-zero derivation in R such that for every x ∊ R, d(x) is algebraic over F of bounded degree. Then R is a primitive ring with a minimal right ideal eR, where e2 = e and eRe is a finite dimensional central division algebra.