α-可逆环的一点注记(英文)

A note on α-reversible rings

设α是环R的自同态。称环R为右α-可逆环,如果对任意的a,b∈R若ab=0,则bα(a)=0.本文讨论了α-可逆环,α-刚性环,可逆环和弱α-Skew Armendariz环的关系。设R是可逆环和右α-可逆环,证明了:(1)R是弱α-Skew Armendariz环;(2)对任意的正整数n, R[x] /(xn)是弱α-Skew Armendariz环;(3)若αt=1R,则R[x;α]是弱Armendariz环.

An endomorphism α of a ring R is called right reversible if whenever ab=0 for a,b∈R,bα（a）=0.A ring R is called right α-reversible if there exists a right reversible endomorphism α of R.The relations between α-reversible,α-rigid,reversible and weak α-skew Armendariz rings are investigated.And it is proven that for reversible and right α-reversible rings R：（1） R is a weak α-skew Armendariz ring;（2） R[x]/（x^n） is a weak α-skew Armendariz ring for any positive integer n;（3） If for some positive integer t,αt=1R,then R[x;α] is weak Armendarizring.