摘要:

LetHbe a Hopf algebra over a fieldk. Under some assumptions onHwe state and prove a generalization of the Wedderburn-Malcev theorem for i7-comodule algebras. We show that our version of this theorem holds for a large enough class of Hopf algebras, such as coordinate rings of completely reducible affine algebraic groups, finite dimensional Hopf algebras over fields of characteristic 0 and group algebras. Some dual results are also included.

ISSN:0092-7872    

DOI:10.1080/00927879908826648

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

A ring is called strongly clean if every element is the sum of an idempotent and a unit which commute. These rings are shown to be a natural generalization of the strongly π-regular rings, and several properties of strongly π-regular rings are extended, including their relationship to Fitting's lemma.

ISSN:0092-7872    

DOI:10.1080/00927879908826649

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Vertex operator representations for toroidal Lie algebras of simply-laced type were studied in [MRY] and [EM]. In this paper we give vertex operator constructions for the toroidal Lie algebra of typeBl(l≥ 3). The constructions are related to the folding of Dynkin diagram ofand a two-cocycle necessary for the vertex operator constructions.

ISSN:0092-7872    

DOI:10.1080/00927879908826650

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Burnside asked questions about periodic groups in his influential paper of 1902. The study of groups with exponent six is a special case of the study of the Burnside questions on which there has been significant progress. It has contributed a number of worthwhile aspects to the theory of groups and in particular to computation related to groups. Finitely generated groups with exponent six are finite. We investigate the nature of relations required to provide proofs of finiteness for some groups with exponent six. We give upper and lower bounds for the number of sixth powers needed to define the largest 2-generator group with exponent six. We solve related questions about other groups with exponent six using substantial computations which we explain.

ISSN:0092-7872    

DOI:10.1080/00927879908826651

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

For a certain class of groups, which are semidirect products arising from an action of a finite rank free abelian group on another group, we study cancellation of the infinite cyclic group in isomorphic direct products. As an application we obtain a sufficient condition for triviality of the genus of certain nilpotent groups.

ISSN:0092-7872    

DOI:10.1080/00927879908826652

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826653

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

Since their introduction in 1964 as a combinatorial tool, incidence algebras have been studied in their own right. In particular, the Jacobson and nilradicals of incidence algebras over commutative rings with identity were determined.Here we present the general radical theory for incidence algebras, with the emphasis on hypernilpotent and subidempotent radicals.

ISSN:0092-7872    

DOI:10.1080/00927879908826654

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In a structural matrix ringMn(ρR) over an arbitrary ringRwe determine the centralizer of the set of matrix units inMn(ρR) associated with the anti-symmetric part of the reflexive and transitive binary relation ρ on {1,2,…,n}. If the underlying ringRhas no proper essential ideal, for example ifRis a field, then we show that the largest ideal ofMn(ρR) contained in the mentioned centralizer coincides with the smallest essential ideal ofMn(ρR).

ISSN:0092-7872    

DOI:10.1080/00927879908826655

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

LetRbe a discrete valuation ring andGa finite group. Let α:G×G→R\{0} be a generalized 2-cocycle, i.e. not necessarily taking its values in the units ofR, and consider the generalized twisted group ringR*αG. In this paper we derive a criterion forR*αG. to be separable over its center. This leads us to study the center and the prime ideals ofR*αG. Furthermore, we give some results on indecomposable modules overR*αG.

ISSN:0092-7872    

DOI:10.1080/00927879908826656

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

We define the Albert algebra of generic matrices and show that its central closure is an Albert division algebra as well as a pure second Tits construction. It contains a cyclic cubic subfield iff this holds true for every Albert division algebra over any extension of the base field.

ISSN:0092-7872    

DOI:10.1080/00927879908826657

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor