{"paper":{"title":"On Radicals of Ore Extensions and Related Questions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Agata Smoktunowicz, Be'eri Greenfeld, Michal Ziembowski","submitted_at":"2017-02-26T22:37:47Z","abstract_excerpt":"We answer several open questions and establish new results concerning differential and skew polynomial ring extensions, with emphasis on radicals. In particular, we prove the following results.\n  If $R$ is prime radical and $\\delta$ is a derivation of $R$, then the differential polynomial ring $R[X;\\delta]$ is locally nilpotent. This answers an open question posed in by Nielsen and Ziembowski.\n  The nil radical of a differential polynomial ring $R[X;\\delta]$ takes the form $I[X;\\delta]$ for some ideal $I$ of $R$, provided that the base field is infinite. This answers an open question posed by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08103","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}