Unitification of Weakly p.q.-Baer *-Rings

TL;DR

This paper introduces weakly principally quasi-Baer *-rings, explores their properties, and provides a partial solution to a unitification problem in *-ring theory, linking these rings to their unital counterparts.

Contribution

It defines weakly principally quasi-Baer *-rings via central covers and establishes their equivalence to principal quasi-Baer *-rings when unital, addressing a longstanding problem.

Findings

Characterization of weakly p.q.-Baer *-rings

Equivalence with p.q.-Baer *-rings with unity

Partial solution to the unitification problem

Abstract

In this paper, we introduce a concept of weakly principally quasi-Baer *-rings in terms of central cover. We prove that a *-rings is a principally quasi-Baer *-rings if and only if it is weakly principally quasi-Baer *-rings with unity. A partial solution to the problem similar to unitification problem raised by S. K. Berberian is obtained.