Non-unital Ore extensions
Volume 172 / 2023
Colloquium Mathematicum 172 (2023), 217-229
MSC: Primary 16S32; Secondary 16S99, 16W70, 16S36, 16U70.
DOI: 10.4064/cm8941-11-2022
Published online: 11 January 2023
Abstract
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 non-zero idempotent. This result generalizes a result by Öinert, Richter and Silvestrov from the unital setting. We also present a family of examples of simple non-unital differential polynomial rings.
