ISSN:0092-7872    

DOI:10.1080/00927877508822036

出版商:Marcel Dekker, Inc.    

年代:1975

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927877508822037

出版商:Marcel Dekker, Inc.    

年代:1975

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927877508822038

出版商:Marcel Dekker, Inc.    

年代:1975

数据来源: Taylor

摘要:

A. W. Chatters [72] has proved a decomposition theorem for a hereditary, Noetherian ring R, namely,where Riis either a prime ring or an Artinian ring. An immediate consequence is a theorem of Small [66] stating that R has a classical right2quotient ring Q(R), since Q(R) = R for any Artinian R, and Q(R) exists for any prime Noetherian ring R by the theorems of Goldie [58, 60] and Lesieur-Croisot [59]. Unfortunately, Chatters’ proof uses a lemma from Small's paper, marring the stated implication. In this paper, we give a another proof of Chatters’ theorem, not only eliminating the dependency on the lemma of Small, but also generalizing it, and a number of other lemmas, from which we deduce a theorem of Camillo and Cozzens [73], characterizing when a left Ore domain is a principal left ideal ring assuming it is a principal right ideal domain.

ISSN:0092-7872    

DOI:10.1080/00927877508822039

出版商:Marcel Dekker, Inc.    

年代:1975

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927877508822040

出版商:Marcel Dekker, Inc.    

年代:1975

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927877508822035

出版商:Marcel Dekker, Inc.    

年代:1975

数据来源: Taylor