Some new characterizations of Normal elements in rings with involution

Abstract

In this paper, we firstly illuminate some properties of normal elements by the consistency of certain equation and construct the group inverses, MP inverses and invertible elements. Then we gives some conditions involving a, a†, a#, a∗, (a#)∗ and (a†)∗ to guarantee that a is normal. Finally, the solution of related equations to depict normality have been studied in a certain set.