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

Abstract

In this paper, we study many new characterizations of PI elements in a rings with involution. Mainly, we first give some necessity and sufficient conditions of PI elements by discussing the solutions of related equations.Next,we discuss some properties of PI elements by constructing univariate and bivariate equations in a fixed set.Finally, we combine PI elements with EP elements,we study the properties of SEP elements with variable equations in a fixed set.