{"paper":{"title":"Bimodules in group graded rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert","submitted_at":"2016-08-30T19:55:56Z","abstract_excerpt":"In this article we introduce the notion of a controlled group graded ring. Let $G$ be a group, with identity element $e$, and let $R=\\oplus_{g\\in G} R_g$ be a unital $G$-graded ring. We say that $R$ is $G$-controlled if there is a one-to-one correspondence between subsets of the group $G$ and (mutually non-isomorphic) $R_e$-bimodules in $R$, given by $G \\supseteq H \\mapsto \\oplus_{h\\in H} R_h$. For strongly $G$-graded rings, the property of being $G$-controlled is stronger than that of being simple. We provide necessary and sufficient conditions for a general $G$-graded ring to be $G$-controll"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08619","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"}