On CNZ ring property via idempotent elements

Abstract

In this paper, the concept of e−CNZ rings is introduced as a generalization of symmetric rings and a particular case of e−reversible rings. Regarding the question of how idempotent elements affect CNZ property of rings. In this note, we show that e−CNZ is not left-right symmetric. We present examples of right e−CNZ rings that are not CNZ and basic properties of right e − CNZ are provided. Some subrings of matrix rings and some extensions of rings such as Jordan extension are investigated in terms of right e−CNZ.