强α-半交换环及其扩张

Strongly α-semicommutative rings and their extensions

设α是环R的一个自同态.如果对任意的a,b∈R,由aα(b)=0(α(a)b=0)可以推出aRb=0,则称R是强右(左)α-半交换环.强右(左)α-半交换环是半交换环的一个子类.给出了强右α-半交换环的几个特征刻画,讨论了它们与相关环的关系,并研究了强右α-半交换环的一些扩张性质.通过引进强α-半交换环的概念,拓宽了半交换环的研究领域.

Letαbe an endomorphism of ring R.A ring Ris called strongly right（left）α-semicommutative if aα（b）=0（α（α）b=0）provides aRb=0for any a,b∈R.The class of strongly right（left）α-semicommutative rings is a subclass of the class of semicommutative rings.Several characterizations of strongly rightα-semicommutative rings are given,the relationships between the strongly rightα-semicommutative rings and related rings are discussed,and some extensions of strongly rightα-semicommutative rings are investigated.We extend the study about semicommutative rings by introducing the concept of stronglyα-semicommutative rings.