Conrad's Partial Order on p.q.-Baer *-Rings

TL;DR

This paper investigates the structure of p.q.-Baer *-rings under Conrads partial order, showing they form a pseudo lattice and characterizing when they are lattices, with initial segments forming orthomodular posets.

Contribution

It establishes that p.q.-Baer *-rings form a pseudo lattice with Conrads partial order and characterizes those that are actual lattices, also analyzing their initial segments.

Findings

p.q.-Baer *-rings form a pseudo lattice under Conrads partial order

Initial segments of these rings are orthomodular posets

Characterization of p.q.-Baer *-rings that are lattices

Abstract

We prove that p.q.-Baer *-ring forms a pseudo lattice with Conrads partial order and also characterize p.q.-Baer *-rings which are lattices. The initial segments of a p.q.-Baer *-ring with Conrads partial order are shown to be orthomodular posets.