{"paper":{"title":"New criteria for a ring to have a semisimple left quotient ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2013-03-04T21:16:21Z","abstract_excerpt":"Goldie's Theorem (1960), which is one of the most important results in Ring Theory, is a criterion for a ring to have a semisimple left quotient ring. The aim of the paper is to give four new criteria (using a completely different approach and new ideas). The first one is based on the recent fact that for an arbitrary ring $R$ the set $\\CM$ of maximal left denominator sets of $R$ is a non-empty set:\n  Theorem (The First Criterion). A ring $R$ has a semisimple left quotient ring $Q$ iff $\\CM $ is a finite set, $\\bigcap_{S\\in \\CM} \\ass (S) =0$ and, for each $S\\in \\CM$, the ring $S^{-1}R$ is a si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0859","kind":"arxiv","version":1},"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"}