{"paper":{"title":"Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"Daniel Gon\\c{c}alves, Danilo Royer, Johan \\\"Oinert, Viviane Beuter","submitted_at":"2017-08-16T16:56:41Z","abstract_excerpt":"Given a partial action $\\pi$ of an inverse semigroup $S$ on a ring $\\mathcal{A}$ one may construct its associated skew inverse semigroup ring $\\mathcal{A} \\rtimes_\\pi S$. Our main result asserts that, when $\\mathcal{A}$ is commutative, the ring $\\mathcal{A} \\rtimes_\\pi S$ is simple if, and only if, $\\mathcal{A}$ is a maximal commutative subring of $\\mathcal{A} \\rtimes_\\pi S$ and $\\mathcal{A}$ is $S$-simple. We apply this result in the context of topological inverse semigroup actions to connect simplicity of the associated skew inverse semigroup ring with topological properties of the action. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04973","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"}