SEP elements and solutions of related equations in a ring with involution

Abstract

In this paper, we study many new characterizations of SEP elements in a rings with involution, mainly, we fifirst discuss some properties of SEP elements by means of regular elements, 1,3-inverses and the equality of certain set. Next, we give some necessity and suffiffifficiency conditions of SEP elements by discussing the solutions of related equations. Finally, we characterize SEP elements by constructing the group inverses and MP inverses.