On some classes of rings and their links

TL;DR

This paper explores various classes of rings, including Armendariz, McCoy, and abelian rings, their interrelations, generalizations, and skew versions involving ring endomorphisms, expanding understanding of their structural properties.

Contribution

It introduces and analyzes generalizations and links among different ring classes, including skew versions, providing new insights into their algebraic relationships.

Findings

Armendariz rings and their relationships with well-known rings

Generalizations of Armendariz rings such as McCoy and abelian rings

Introduction of skew versions of ring classes with respect to endomorphisms

Abstract

The paper deals with Armendariz rings, their relationships with some well known rings. Then we treat generalizations of Armendariz rings, such as McCoy ring, abelian ring and their links. We also consider a skew version of some classes of rings, with respect to a ring endomorphism $\alpha. $