The Wedderburn-Artin Theorem

TL;DR

This paper provides a concise, module-free proof of the Wedderburn-Artin theorem, demonstrating that simple left artinian rings are isomorphic to matrix rings over division rings.

Contribution

It offers a new, self-contained proof of the Wedderburn-Artin theorem that avoids the traditional module-based approach.

Findings

Proof is shorter and more accessible

Clarifies the structure of simple left artinian rings

Enhances understanding of ring isomorphisms

Abstract

The celebrated Wedderburn-Artin theorem states that a simple left artinian ring is isomorphic to the ring of matrices over a division ring. We give a short and self-contained proof which avoids the use of modules.