{"paper":{"title":"Simplicity of partial skew group rings and maximal commutativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.OA","authors_text":"Daniel Gon\\c{c}alves, Danilo Royer, Johan \\\"Oinert","submitted_at":"2013-06-19T19:19:56Z","abstract_excerpt":"Let R0 be a commutative associative ring (not necessarily unital), G a group and alpha a partial action by ideals that contain local units. We show that R0 is maximal commutative in the partial skew group ring R0*G if and only if R0 has the ideal intersection property in R0*G. From this we derive a criterion for simplicity of R0*G in terms of maximal commutativity and $G-$simplicity of R0 and apply this to two examples, namely to partial actions by clopen subsets of a compact set and to give a new proof of the simplicity criterion for Leavitt path algebras. A new proof of the Cuntz-Krieger uni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4648","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"}