ISSN:0092-7872    

DOI:10.1080/00927879908826630

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetRbe a right τ-noetherian ring, where τ denotes a hereditary torsion theory on the category of rightR-modules. It is shown that every essential τ-closed right ideal of every prime homomorphic image ofRcontains a nonzero two-sided ideal if and only if any two τ-torsionfree injective indecomposable rightR-modules with identical associated prime ideals are isomorphic, and for any τ-closed prime idealPthe annhilator of a finitely generatedP-tame rightR-module cannot be a prime ideal properly contained inP. Furthermore, if in the last condition finitely generated is replaced by r-noetherian, then all τ-noetherian τ-torsionfree modules turn out to be finitely annihilated.

ISSN:0092-7872    

DOI:10.1080/00927879908826631

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetRbe a unit-regular ring , letXbe the set of all nonzero, nonunits ofRand letGbe the group of all units ofR. In this paper, some finiteness properties ofRare investigated by considering group actions ofGonXas follows:First, in case of half-transitive regualr action if 2 is unit inRor the number of idempotents inRis finite, thenRis finite. Secondly, ifGis cyclic and 2 is unit inR, then every orbit under regualr action is a finite set, and so in this case, ifRhas a finite number of idempotents, thenRis finite. Finally, ifFis a field in which 2 is unit and the multiplicative group of all nonzero elenents inFforms a cyclic group, thenFis finite.

ISSN:0092-7872    

DOI:10.1080/00927879908826632

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826633

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Various representation-theoretic parameters of a finite group are shown to satisfy formulas similar to formulas appearing in reformulations by Kölshammer, Robinson, and Thévenaz of Alperin's Conjecture. The conjecture itself is reformulated again, now as a statement not mentioning characters or conjugacy classes.

ISSN:0092-7872    

DOI:10.1080/00927879908826634

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

An algebra of rank three is a commutative, finite dimensional algebra that may be defined by the property that every element generates a subalgebra of dimension not greater than two. In this article we discuss several classes of such algebras, including two classes related to central simple Jordan algebras, and derive some general results which indicate that, with the exception of one pathological class related to nilpotent algebras, every rank three algebra can be constructed either from a quadratic and alternative algebra or from a representation of a Clifford algebra. Among other results, semisimple and simple rank three algebras are characterized, and the radical of an arbitrary rank three algebra is determined.

ISSN:0092-7872    

DOI:10.1080/00927879908826635

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Letlbe an odd integerl>1 and let ϵ be a primitivelth-root of unity. In this paper we prove that everyUϵ(sl(n))-irreducible module parametrized by a spherical, unipotent conjugacy class О of SL(n) has dimension divisible byl½dimОresuit was conjectured by De Concini, Kac and Procesi in [DC-K-P 1].

ISSN:0092-7872    

DOI:10.1080/00927879908826636

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826637

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetFbe a field of any characteristic. Forn≥ 0, let.The degree conjecture asserts that for eachn≥0Letpbe anyn-fold quadratic Pfister form overFandF(p) the function field ofp. Then the function field conjecture assertsWe prove that (DC) is equivalent to (FFC).

ISSN:0092-7872    

DOI:10.1080/00927879908826638

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

We use the BEST theorem in Graph Theory to study a non-alternating version of the standard identity in prime characteristic. Using these re-sults and the linearized Hamilton-Cayley identity, we show the existence of an element with reduced trace 1.

ISSN:0092-7872    

DOI:10.1080/00927879908826639

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor