On p-Symmetric Rings

Abstract

This article embodies the notion of p-symmetric rings using the concept of non-
zero potent elements in a ring. It is proved that R is a p-symmetric ring if and only if
pn−1Rpn−1 is a symmetric ring and pn−1 is left semicentral. Moreover, p-symmetric
rings in terms of upper triangular matrix rings and left min-p-abel rings have been
characterized. Furthermore, we introduce strongly p-symmetric ring and also pro-
vide a characterization of strongly p-symmetric rings in terms of strongly left min-
p-abel rings. In particular, it is proved that R is a strongly left min-p-abel ring if and
only if R is a strongly p-symmetric ring for each pn−1 ∈ MPl (R). Further, the notion
of p-reduced ring as a subclass of reduced ring is derived and right p-reduced rings
are p-symmetric rings have been established.