A Study on Tri Reversible Rings

This article embodies a ring theoretic property which, preserves the reversibility of elements at non-zero tripotents. A ring R is defined as quasi tri reversible if any non-zero tripotent element ab of R implies ba is also a tripotent element in R for a, b ∈ R. We explore the quasi tri reversibility of 2 by 2 full and upper triangular matrix rings over various kinds of reversible rings, deducing that the quasi tri reversibility is a proper generalization of reversible rings. It is proved that the polynomial rings are not quasi tri reversible rings. The relation of symmetric rings, IF P and Abelian rings with reversibility and quasi tri reversibility arestudied. It is also observed that the structure of weakly tri normal rings and quasi tri reversible rings are independent of each other.