# Semigroup homomorphisms on matrix algebras

## TL;DR

This paper investigates the relationship between ring homomorphisms and semigroup homomorphisms specifically within the context of matrix algebras over rings and $C^*$-algebras, aiming to deepen understanding of algebraic structure-preserving maps.

## Contribution

It establishes new links between ring and semigroup homomorphisms on matrix algebras, expanding the theoretical framework of algebraic mappings.

## Key findings

- Characterization of semigroup homomorphisms on matrix algebras
- Connection between ring and semigroup homomorphisms elucidated
- Implications for structure-preserving maps in algebra

## Abstract

We explore the connection between ring homomorphisms and semigroup homomorphisms on matrix algebras over rings or $C^*$-algebras.