New characterizations of EP, generalized normal and generalized Hermitian elements in rings

Abstract

We present a number of new characterizations of EP elements in rings with involution in purely algebraic terms. Then, we study equivalent conditions for an element a in a ring with involution to satisfy a na = aa n or a n = (a) n for arbitrary n ∈ N. For n = 1, we present some new characterizations of normal and Hermitian elements in rings with involution. © 2011 Elsevier Inc. All rights reserved.