CHARACTERIZATIONS OF t2-REVERSIBLE RINGS

Abstract

This article aims to investigate the ring theoretic structures of (strongly) t2-reversible ring using the concept of non-zero tripotent elements. A ring R is said to be t2-reversible if ab = 0 implies bat2 = 0 for all a,b ∈ R and t is a non-zero tripotent element of R. It is proved that R is a t2-reversible ring if and only if t2 is left semicentral and t2Rt2 is a reversible ring. We also introduce and establish several characteristics of strongly t2-reversible rings. It is proved that every strongly t2-reversible ring is also a t2-reversible ring but the converse need not be true. Moreover we call, R is a right (left) t2-reduced ring if N(R)t2 = 0 (t2N(R) = 0), where N(R) stands for the set of all nilpotent elements of R and we have established some of its properties.