نویسندگان | K. Paykan, M. Habibi, A. Parsian |
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نشریه | Communications in Algebra |
ارائه به نام دانشگاه | Tafresh University |
نوع مقاله | Full Paper |
تاریخ انتشار | May 2024 |
رتبه نشریه | ISI (WOS) |
نوع نشریه | چاپی |
کشور محل چاپ | ایالات متحدهٔ امریکا |
نمایه نشریه | Taylor & Francis |
چکیده مقاله
Let $R$ be a ring with a monomorphism $\alpha$ and an $\alpha$-derivation $\delta$. In this article, we give a simple and different proof about the semiprimitivity of Ore extensions which states that the skew polynomial ring $R[x; \alpha,\delta ]$ is semiprimitive reduced if and only if $R$ is $\alpha$-rigid. This unifies and extends a number of known results on the Jacobson radical in the special cases. Also, as an application of our results, by imposing constraints on $\alpha$ and $\delta$, we completely identify the Jacobson radical of rings whose the set of all nilpotent elements has special conditions. Important examples are provided to illustrate the applications of the results.