Some characterizations of strongly π-regular rings

Abstract

A ring R is said to be strongly π-regular if for every aR there exist a positive integers n, bR such that an = an+1b.  In this paper it has been proved that an abalian ring R is strongly π-regular if and only the set of all nilpotent element of R coincide with the Jacobson radical and R/J(R) is strongly-regular. In this study, some other characterizations of this kind of rings have been investigated and explored.