# On Lenagan's Theorem for finite length bimodules

## TL;DR

This paper provides a self-contained proof of Lenagan's Theorem for finite length bimodules, avoiding reliance on Goldie's Theorem, thereby simplifying the theoretical framework.

## Contribution

It introduces a new, independent proof of Lenagan's Theorem that does not depend on Goldie's Theorem, enhancing understanding of bimodule theory.

## Key findings

- Proof of Lenagan's Theorem without Goldie's Theorem
- Simplified theoretical approach to finite length bimodules
- Potential for broader application in module theory

## Abstract

We offer a self-contained proof of Lenagan's Theorem which does not rely on Goldie's Theorem