Non-unital Ore extensions

TL;DR

This paper characterizes simple non-unital differential polynomial rings over s-unital rings with nonzero idempotent kernels, extending known results from unital rings and providing new examples.

Contribution

It generalizes the classification of simple differential polynomial rings to the non-unital setting with specific conditions.

Findings

Characterization of simple non-unital differential polynomial rings

Extension of unital results to non-unital rings

Construction of new examples of simple non-unital rings

Abstract

In this article, we study Ore extensions of non-unital associative rings. We provide a characterization of simple non-unital differential polynomial rings $R[x;\delta]$, under the hypothesis that $R$ is $s$-unital and $\ker(\delta)$ contains a nonzero idempotent. This result generalizes a result by \"Oinert, Richter and Silvestrov from the unital setting. We also present a family of examples of simple non-unital differential polynomial rings.