广义可逆环

GENERALIZED REVERSIBLE RINGS

设R是环,环R的自同态α称为可逆的,如果对任意a,b∈R,若ab=0,则α(b)a=0.环R称为α-可逆环,如果R存在可逆的自同态α.本文将可逆环的结论推广到α-可逆环上,另外证明了斜幂级数环(简单地记为sps环)和Armendariz环的推广α-sps Armendariz环R[[x;α]]的Baer性和右p.p.性.

For an endomorphism α of a ring R,the endomorphism α is called reversible if ab=0 implying α（b）a=0 for any a,b∈R.A ring R is called α-reversible if there exists a reversible endomorphism α of R.In this paper,various results of reversible rings are extended to α-reversible rings.In addition,the Baerness and the right p.p.-property of an α-sps Armendariz ring R were introduced,which was generalization of both skew power series rings and Armendariz rings.