摘要
推广了弱对称环的概念,研究了具有弱对称自同态α的环,称为弱对称α-环,讨论弱对称α-环与相关环的关系,研究了弱对称α-环的一些扩张性质。证明了:(1)设α是环R的自同态,则R是α-rigid环当且仅当R是弱对称α-环,且由aRα(a)∈nil(R)可推出a=0,对任何a∈R;(2)设R是半交换环,α是R的自同态,则R是弱对称α-环当且仅当R[x]是弱珔α-sy环。
The notion of weakly symmetric α-rings, which is rings with weakly symmetric endomorphismα, is intro-duced, and the study of weakly symmetric rings is extended.The relationships between weakly symmetric α-rings and related rings are discussed and some extensions of weakly symmetricα-rings are investigated.It is showed that （1） Letαbe an endomorphism of a ring R.Then R isα-rigid if and only if R is weakly symmetricα-ring and aRα（ a）∈nil（ R） implies a=0 for any a∈R; （2） Let R be a semicommutative ring and αan endomorphism of R.Then R is weakly symmetricα-ring if and only if R[ x] is weakly symmetric ā-ring.
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2014年第2期12-17,28,共7页
Journal of Shandong University(Natural Science)
基金
国家自然科学基金资助项目(11101217)
