Right Central CNZ Property Skewed by Ring Endomorphisms

Abstract

The concept of the reversible ring property concerning nilpotent elements was introduced by A.M. Abdul-Jabbar and C. A. Ahmed, who introduced the concept of commutativity of nilpotent elements at zero, termed as a CNZ ring, as an extension of reversible rings. In this paper, we extend the CNZ property through the influence of a central ring endomorphism alpha , introducing a new type of ring called a right alpha -skew central CNZ ring. This concept not only expands upon CNZ rings but also serves as a generalization of right alpha -skew central reversible rings. We explore various properties of these rings and delve into extensions of right alpha -skew central CNZ rings, along with examining several established results, which emerge as corollaries of our findings.