m-weak group inverses in a ring with involution

TL;DR

This paper investigates the uniqueness of m-weak group inverses in rings with involution, establishing conditions for their uniqueness and exploring their properties.

Contribution

It introduces the concept of m-weak group inverse in rings with involution and analyzes conditions for its uniqueness and properties.

Findings

Uniqueness of weak group inverse linked to idempotent elements.

Definition and properties of m-weak group inverse.

Conditions under which each element has at most one m-weak group inverse.

Abstract

In a unitary ring with involution, we prove that each element has at most one weak group inverse if and only if each idempotent element has a unique weak group inverse. Furthermore, we define the $m$-weak group inverse and show some properties of $m$-weak group inverse.