Centeral Armendariz rings relative to a monoid

TL;DR

This paper introduces and explores the properties of central Armendariz rings relative to monoids, generalizing existing concepts and establishing conditions under which these rings are commutative or monoids are cancellative.

Contribution

It defines the notion of M-central Armendariz rings relative to monoids and investigates their properties, extending the theory of central Armendariz rings.

Findings

If R is central reduced, then R is M-central Armendariz for a u.p.-monoid M.

An M-central Armendariz ring is either commutative or M is cancellative.

Provides examples illustrating the properties and boundaries of these rings.

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.