{"paper":{"title":"Graded differential polynomial rings","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Yassine Ait Mohamed","submitted_at":"2026-06-22T13:54:24Z","abstract_excerpt":"Let $R$ be a $\\Gamma$-graded ring and $\\delta$ a derivation of $R$. We determine exactly when the differential polynomial ring $R[t;\\delta]$ admits a grading compatible with that of $R$: this happens if and only if $\\delta$ is a $\\gamma$-derivation for some $\\gamma$ in the centralizer of the support, in which case the grading is explicit and unique once $\\deg(t)$ is fixed. Over an arbitrary group, we establish graded analogues of the classical simplicity, primeness, and Noetherianity theorems; in characteristic zero, $R[t;\\delta]$ is gr-simple if and only if $R$ is $\\delta$-gr-simple and $\\del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23352","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23352/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}