On differential polynomial rings with locally nilpotent derivations

Jooyoung Shin

On differential polynomial rings with locally nilpotent derivations

Rings and Algebras 2023-12-18 v2

Authors: Jooyoung Shin

Abstract

Let $R$ be a $\mathbb{Q}$ -algebra and $d$ be a locally nilpotent derivation on $R$ . We will show that the Jacobson radical of a differential polynomial ring $R[x;d]$ equals $I[x;d]$ where $I$ is a nil ideal of $R$ . This answers a question posed by Agata Smoktunowicz.

Keywords

differential polynomial ring locally nilpotent derivation jacobson radical nil ideal q-algebra

Cite

@article{arxiv.2305.19464,
  title  = {On differential polynomial rings with locally nilpotent derivations},
  author = {Jooyoung Shin},
  journal= {arXiv preprint arXiv:2305.19464},
  year   = {2023}
}

Comments

Lemma 3 is incorrect

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