{"paper":{"title":"The largest left quotient ring of a ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2011-01-26T17:03:53Z","abstract_excerpt":"The left quotient ring (i.e. the left classical ring of fractions) $Q_{cl}(R)$ of a ring $R$ does not always exist and still, in general, there is no good understanding of the reason why this happens. In this paper, it is proved existence of the largest left quotient ring $Q_l(R)$, i.e. $Q_l(R) = S_0(R)^{-1}R$ where $S_0(R)$ is the largest left regular denominator set of $R$. It is proved that $Q_l(Q_l(R))=Q_l(R)$; the ring $Q_l(R)$ is semi-simple iff $Q_{cl}(R)$ exists and is semi-simple; moreover, if the ring $Q_l(R)$ is left artinian then $Q_{cl}(R)$ exists and $Q_l(R) = Q_{cl}(R)$. The gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5107","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"}