Centeral Armendariz rings relative to a monoid

Abstract

In this paper, the notion of central Armendariz rings relative to a monoid is introduced which is a generalization of central Armendariz rings and investigate their properties. It is shown that if R is central reduced, then R is M-central Armendariz for a u.p.-monoid M. For a monoid M and ring R, we prove if R is an M-central Armendariz, then either R is commutative or M is cancellative. Various examples which illustrate and delimit the results of this paper are provided.