{"paper":{"title":"Simplicity of algebras via epsilon-strong systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Patrik Nystedt","submitted_at":"2018-05-30T13:44:51Z","abstract_excerpt":"We obtain sufficient criteria for simplicity of systems, that is, rings $R$ that are equipped with a family of additive subgroups $R_s$, for $s \\in S$, where $S$ is a semigroup, satisfying $R = \\sum_{s \\in S} R_s$ and $R_s R_t \\subseteq R_{st}$, for $s,t \\in S$. These criteria are specialized to obtain sufficient criteria for simplicity of, what we call, s-unital epsilon-strong systems, that is systems where $S$ is an inverse semigroup, $R$ is coherent, in the sense that for all $s,t \\in S$ with $s \\leq t$, the inclusion $R_s \\subseteq R_t$ holds, and for each $s \\in S$, the $R_s R_{s^*}$-$R_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11955","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"}