ISSN:0092-7872    

DOI:10.1080/00927879208824453

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824454

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

A unital leftR-moduleRMis said to have property (S) if every surjective endomorphism ofRMis an automorphism, the ringRis called left (right)S-ring if every left (right)R-module with property (S) is Noetherian,Ris calledS-ring if it is both a left and a rightS-ring. In this note we show that a duo ring is a leftS-ring if and only if it is left Artinian left principal ideal ring. To do this we shall construct on every non distributive Artinian local ring with radical square zero a non-finitely generated module with property (S). And we give an example of left duo left Artinian left principal ideal ring which is not a leftS-ring, showing the necessity of the ring to be duo in the above result.

ISSN:0092-7872    

DOI:10.1080/00927879208824455

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Letkbe a field of characteristicp>0 and D≠0 a family ofk-derivations ofk[x,y]. It is proved in [1] thatk[x,y]D, the ring of constants with respect to D, can be generated, as ak[xp,yp]-algebra, byp- 1 elements. In this note we prove thatp- 1 is the sharp upper bound of numbers of generators.

ISSN:0092-7872    

DOI:10.1080/00927879208824456

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824457

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824458

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824459

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

The notion of a simple ring DGderived from a group ring KG is introduced in case K is a field and G is an infinite residually finite group. The close link between DGand KGis exploited in both directions: first, for a simple proof of the Kaplansky's conjecture concerning direct finiteness of KG. Second, to show that DGprovides counter-examples to some conjectures dealing with von Neumann regular rings and the rings all of whose one-sided ideals are generated by idempotents.

ISSN:0092-7872    

DOI:10.1080/00927879208824460

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824461

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879208824462

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor