摘要:

Abstract length functions on groups were introduced by Lyndon [5]. In [2] Chiswell showed that for a group action on an IR-tree there is a length function associated with each point of the tree, and moreover any length function can occur in this way. This paper establishes necessary and sufficient conditions for two length functions to arise from the same action of a group on a tree.

ISSN:0092-7872    

DOI:10.1080/00927879408824847

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

We give a short proof of theorems of Kaplansky and Slin'ko concerning the bounded degree of certain associative or Jordan algebraic topological algebras. This new proof even works forpower-associativealgebras.

ISSN:0092-7872    

DOI:10.1080/00927879408824848

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824849

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824850

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

It is well-known that a ring with no nonzero nilpotent elements - a so-called reduced ring - is a subdirect product of domains. Moreover, as we have recently shown [2], a prime ring with only finitely many nilpotent elements is either a domain or is finite. In view of these results, it is natural to ask what can be said in general about rings with only finitefy many nilpotent elements. A crucial property of such rings is that they contain no infinite zero subrings, hence we are led to consider rings with this property also. Our principal result is that for any ring R with only finitely many nilpotent elementsis a direct sum of a reduced ring and a finite ring, where p(R) denotes the prime radical of R. One consequence is a finiteness theorem for periodic rings; another is the rather surprising result that every ring with infinitely many nilpotent elements has an infinite zero subring.

ISSN:0092-7872    

DOI:10.1080/00927879408824851

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824852

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824826

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor