On Extended Reversible Rings

Abstract

An endomorphism alpha of a ring R is called right reversible if whenever ab = 0 for a, b is an element of R, then b alpha(a) = 0. A ring R is called right alpha-reversible if there exists a right reversible endomorphism alpha of R. The notion of an alpha-reversible ring is a generalization of alpha-rigid rings as well as an extension of reversible rings. We study characterizations of alpha-reversible rings and their related properties including extensions. The relationship between alpha-reversible rings and generalized Armendariz rings is also investigated. Several known results relating to alpha-rigid and reduced rings can be obtained as corollaries of our results.