中文摘要：

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α珔-sy环。

英文摘要：

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.