Sorry, the nilpotents are in the center

TL;DR

This paper proves that a finite ring is commutative if all its nilpotent elements are in the center, providing a simplified proof of a well-known algebraic result.

Contribution

It offers a straightforward proof of a classic theorem linking nilpotent elements and ring commutativity in finite rings.

Findings

Finite rings are commutative when all nilpotents are central.

The proof simplifies understanding of the structure of nilpotent elements.

Highlights the importance of nilpotents in determining ring properties.

Abstract

The behavior of nilpotents can reveal valuable information about the algebra. We give a simple proof of a classic result that a finite ring is commutative if all its nilpotents lie in the center.