{"paper":{"title":"The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OA"],"primary_cat":"math.RA","authors_text":"Daniel Gon\\c{c}alves, Dirceu Bagio, Johan \\\"Oinert, Paula Savana Est\\'acio Moreira","submitted_at":"2022-11-23T16:02:28Z","abstract_excerpt":"Given a partial action $\\alpha$ of a groupoid $G$ on a ring $R$, we study the associated partial skew groupoid ring $R \\rtimes_{\\alpha} G$, which carries a natural $G$-grading. We show that there is a one-to-one correspondence between the $G$-invariant ideals of $R$ and the graded ideals of the $G$-graded ring $R \\rtimes_{\\alpha}G.$ We provide sufficient conditions for primeness, and necessary and sufficient conditions for simplicity of $R \\rtimes_{\\alpha}G.$ We show that every ideal of $R \\rtimes_{\\alpha}G$ is graded if, and only if, $\\alpha$ has the residual intersection property. Furthermor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.13071","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.13071/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"}