# Unit-regularity and representability for semiartinian *-regular rings

## TL;DR

This paper proves that semiartinian subdirectly irreducible *-regular rings can be represented within inner product spaces, linking algebraic properties to geometric representations.

## Contribution

It establishes the representability of a class of *-regular rings, specifically semiartinian subdirectly irreducible ones, within inner product spaces, which was previously unknown.

## Key findings

- Semiartinian subdirectly irreducible *-regular rings are representable in inner product spaces.
- The result connects algebraic structure with geometric representation.
- Provides a new perspective on the structure of *-regular rings.

## Abstract

We show that any semiartinian subdirectly irreducible *-regular ring R admits a representation within some inner product space.