查看文章

An endomorphism α of a ring R is called weak reversible if whenever the product of any two elements of a ring R, ab, is a nilpotent element of R, then so is the bα (a). A ring R is called weak α-reversible if there exist a weak reversible endomorphism a of R. The notion of weak α-reversible ring is a generalization of α-compatible rings as well as an extension of reversible rings. A number of properties of this generalization are established, and connections of properties of a this ring R with those of the ring R [x; α] are investigated. As a consequence, several known results relating to α-compatible and α-rigid rings can be obtained as corollaries of our results.