# Representations of *-regular rings and their ortholattices of projections

## TL;DR

This paper demonstrates that subdirectly irreducible *-regular rings can be represented within inner product spaces if their ortholattice of projections can also be represented, linking algebraic and lattice-theoretic structures.

## Contribution

It establishes a connection between the representability of *-regular rings and their ortholattices of projections, providing new insights into their structural relationship.

## Key findings

- Subdirectly irreducible *-regular rings admit inner product space representations.
- Representation of the ortholattice of projections is key to representing the ring.
- The work bridges algebraic and lattice-theoretic perspectives in *-regular rings.

## Abstract

We show that a subdirectly irreducible *-regular ring admits a representation within some inner product space provided so does its ortholattice of projections.