{"paper":{"title":"Differential polynomial rings over rings satisfying a polynomial identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Blake W. Madill, Forte Shinko, Jason P. Bell","submitted_at":"2014-03-10T12:57:29Z","abstract_excerpt":"Let $R$ be a ring satisfying a polynomial identity and let $\\delta$ be a derivation of $R$. We show that if $N$ is the nil radical of $R$ then $\\delta(N)\\subseteq N$ and the Jacobson radical of $R[x;\\delta]$ is equal to $N[x;\\delta]$. As a consequence, we have that if $R$ is locally nilpotent then $R[x;\\delta]$ is locally nilpotent. This affirmatively answers a question of Smoktunowicz and Ziembowski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2230","kind":"arxiv","version":2},"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"}