An idempotent ring cannot be Morita equivalent to its ideal

TL;DR

This paper proves that an idempotent ring cannot be Morita equivalent to any of its proper idempotent ideals, highlighting a fundamental limitation in the structure of such rings.

Contribution

It establishes a new theoretical result showing the impossibility of Morita equivalence between an idempotent ring and its proper ideal.

Findings

Idempotent rings are not Morita equivalent to their proper idempotent ideals.

The result clarifies structural constraints in ring theory.

This contributes to the understanding of Morita equivalence in algebra.

Abstract

In this note it is proven that an idempotent ring cannot be Morita equivalent to its idempotent proper ideal.