{"paper":{"title":"Non-associative Ore extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert, Johan Richter, Patrik Nystedt","submitted_at":"2015-09-04T13:11:25Z","abstract_excerpt":"We introduce non-associative Ore extensions, $S = R[X ; \\sigma , \\delta]$, for any non-associative unital ring $R$ and any additive maps $\\sigma,\\delta : R \\rightarrow R$ satisfying $\\sigma(1)=1$ and $\\delta(1)=0$. In the special case when $\\delta$ is either left or right $R_{\\delta}$-linear, where $R_{\\delta} = \\ker(\\delta)$, and $R$ is $\\delta$-simple, i.e. $\\{ 0 \\}$ and $R$ are the only $\\delta$-invariant ideals of $R$, we determine the ideal structure of the non-associative differential polynomial ring $D = R[X ; \\mathrm{id}_R , \\delta]$. Namely, in that case, we show that all ideals of $D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01436","kind":"arxiv","version":3},"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"}