Characterize EP elements via w-core inverses

Abstract

Let $R$ be a ring with an involution. It has been proven that $a\in R^{\rm EP}$ if and only if $(aa^\#)^*=aa^\#$, where $a^\#$ is the group inverse of $a$, and $R^{\rm EP}$ is the set of all EP elements in $R$. In this paper, we use $w$-core inverses and core inverses to describe EP elements in a ring with an involution, by making full use of the result mentioned before.