A study on Tri reversible Rings

Document Type : Original Manuscript


1 Gauhati University, Guwahati

2 Department of mathematics, Gauhati University, India



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 are
studied. It is also observed that the structure of weakly tri normal
rings and quasi tri reversible rings are independent of each other.