{"paper":{"title":"The largest strong left quotient ring of a ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2013-10-03T19:54:17Z","abstract_excerpt":"For an arbitrary ring $R$, the largest strong left quotient ring $Q_l^s(R)$ of $R$ and the strong left localization radical $\\glsR$ are introduced and their properties are studied in detail. In particular, it is proved that $Q_l^s(Q_l^s(R))\\simeq Q_l^s(R)$, $\\gll^s_{R/\\glsR}=0$ and a criterion is given for the ring $ Q_l^s(R)$ to be a semisimple ring. There is a canonical homomorphism from the classical left quotient ring $Q_{l, cl}(R)$ to $Q_l^s(R)$ which is not an isomorphism, in general. The objects $Q_l^s(R)$ and $\\gll^s_R$ are explicitly described for several large classes of rings (semip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1077","kind":"arxiv","version":3},"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"}