Trivial extension of armendariz rings and related concepts

Abstract EN

This paper investigate the possibility of inheriting the properties of the ring R to the trivial extension ring R(R,R) and present the relationship between the trivial extension R(R,R) and many types of rings.

The concepts of 2-primal, reversible, central reversible, semicommutative, nil–semicommutative, π-Armendariz and central π-Armendariz rings are studied with trivial extension R(R,R) and some characterizations of -Armendariz and central π-Armendariz rings are given.