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 n a ∗  =  a ∗ a 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.