ISSN:0092-7872    

DOI:10.1080/00927870008827060

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Given a leftR-moduleM, we study the connection between the (right and left) properties of its endomorphism ringS=End(RM)and the properties of the category σf[M] of all submodules of finitelyM-generated leftR-modules.

ISSN:0092-7872    

DOI:10.1080/00927870008827061

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827062

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827063

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827064

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In this paper, we show that a ringRsatisfies unit 1-stable range if and only ifa1R+ ⋯ +amR=dRwithm≥ 2,a1, ⋯amϵRimplies that there existu1, ⋯umϵU(R) such thata1u1+⋯+amum= d and an exchange ringRhas stable range one if and only ifa1R+⋯+amR=dRwithm≥ 2,a1,⋯,amϵRimplies that there exist unit-regularw1,⋯,wmϵRsuch thata1w1+⋯+amwm= d. Also we show that an exchange ringRsatisfies then-stable range condition if and only ifa(nR)+bR=dRwithaϵRn,b,dϵRimplies that there exist unimodular regularwϵnRand:yϵRsuch thataw+by = d.

ISSN:0092-7872    

DOI:10.1080/00927870008827065

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetAbe a prime ring with maximal right ring of quotientsQand with extended centroidC. Further, letSbe a set, let αS→Abe a map, letmbe a positive integer and letEiFiSm-1, be maps. We study functional identities of the formfor alls1,s2,⋯,smϵS(where, etc). If Sαis an (m+ l)-free subset ofQ(for example, ifSα=AandAis not algebraic of bounded degreem+1 overC, orSαis a ncentral Lie ideal ofAandAis not algebraic of bounded degreem+ 2 overC), definitive results are obtained.

ISSN:0092-7872    

DOI:10.1080/00927870008827066

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We show that a map in several variables on a prime ring satisfying an identity of polynomial type must be a quasi-polynomial (i.e., a polynomial in noncommutative variables whose coefficients are Martindale centroid valued functions)provided that the ring does not satisfy a standard identity of low degree. Obtained results have applications to the study of Lie maps of prime rings (Lie ideals of prime rings and skew elements of prime rings with involution)and to the study of Lie-admissible algebras and Lie homomorphisms of Lie algebras of Poisson algebras.

ISSN:0092-7872    

DOI:10.1080/00927870008827067

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827068

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

The aim of this paper is to give a new and direct proof of the theorem.

ISSN:0092-7872    

DOI:10.1080/00927870008827069

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor