A Note on Noncommutative Even Square Rings

TL;DR

This paper determines the smallest size of a noncommutative even square ring, showing it is a nil ring with characteristic four, primarily using illustrative examples.

Contribution

It identifies the minimal order of noncommutative even square rings and characterizes their algebraic properties, such as being nil rings with characteristic four.

Findings

Least order of noncommutative even square rings identified

Such rings are nil rings with characteristic four

Main proof relies on specific examples

Abstract

In this note we find the least order of a noncommutative even square ring and we note that it is a nil ring having characteristic four. In order to prove the main result given in this note we mainly use suitable examples.