REGULARITY OF RINGS WITH INVOLUTION

Abstract

The compact methodology of studying ∗-rings, is to study them in its own independent category. In this paper we continue the study of ∗-rings and get the involutive definition of regularity of elements which is compatible with the definition of *-regular *-rigs given by Kaplansky and Berberian. We introduce also both strongly ∗-regular ∗-rings and the concept of ∗-regular pairs which works as a weak definition of invertibility of element.