-Skew -McCoy Rings

Abstract

As a generalization of -skew McCoy rings, we introduce the concept of -skew -McCoy rings, and we study the relationships with another two new generalizations, -skew -McCoy rings and -skew -McCoy rings, observing the relations with -skew McCoy rings, -McCoy rings, -skew Armendariz rings, -regular rings, and other kinds of rings. Also, we investigate conditions such that -skew -McCoy rings imply -skew -McCoy rings and -skew -McCoy rings. We show that in the case where is a nonreduced ring, if is 2-primal, then is an -skew -McCoy ring. And, let be a weak ()-compatible ring; if is an -skew -McCoy ring, then is -skew -McCoy.