ISSN:0092-7872    

DOI:10.1080/00927879908826751

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In this paper, we shall present a general process for structure presheaves of general rings which are not necessarily left noetherian nor commutative. We shall give several necessary and sufficient conditions such that the structure presheaves are actually sheaves. These results generalize considerably Grothendieck’s original one. as well as various existing corresponding results.

ISSN:0092-7872    

DOI:10.1080/00927879908826752

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826753

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826754

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826755

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In several branches of representation theory, the existence of Auslander-Reiten sequences has led to new structural insights. for example, in the module theory of artinian algebras [11, 6], in the theory of lattices over classical orders [18, 2] over a complete discrete valuation domainR, and for the corresponding derived categories [12, 17]. For anR-order ⋀ in a finite dimentional algebraAover the quotient fieldKofR, Auslander and Reiten [2, 5] have charaterized the non-projective indecomposable ⋀-latticeEfor which an Auslander-Reiten sequence (AR-sequence for short)L→H→Eexists as those ⋀-latticesA-moduleKEis projective.

ISSN:0092-7872    

DOI:10.1080/00927879908826756

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

For a henselian local ringR, Azurnaya [3] proved that every module-finiteR-algebraRwithR/RadAseparable admits an inertial algebra, that is. a separable subalgebraBwithB+ RadA=A, and he showed thatBis unique up to conjugation. This fundamental theorem has been a starting point for intensive research on inertial algebras, with major contributions by Ingraham [10, 16. 17, 18], Brown [7, 8, 9, 10], Kirkman [19], Wehlen [25, 26, 27], Cipolla [11, 12], Deneen [14]. and others.

ISSN:0092-7872    

DOI:10.1080/00927879908826757

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879908826758

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

We introduce procellular algebras, so called because they are inverse limits of finite dimensional cellular algebras as defined by Graham and Lehrer. A procellular algebra is defined as a certain completion of an infinite dimensional cellular algebra whose cell datum is of “proflnite type”. We show how these notions overcome some known obstructions to the theory of cellular agebras in infinite dimensions.

ISSN:0092-7872    

DOI:10.1080/00927879908826759

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor

摘要:

In earlier papers it has been shown that certain different types of conditions on the factors in a factorization of a finite abelian group by its subsets lead to the conclusion that one factor must be a subgroup. In this paper the common generalization is proved that this result still holds even if different factors satisfy different types of condition. It is also shown that one condition may be weakened without effecting the conclusion.

ISSN:0092-7872    

DOI:10.1080/00927879908826760

出版商:Gordon and Breach Science Publishers Ltd.    

年代:1999

数据来源: Taylor