{"paper":{"title":"Tor-pairs: products and approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Manuel Cort\\'es Izurdiaga","submitted_at":"2019-07-17T14:36:26Z","abstract_excerpt":"Recently the author has studied rings for which products of flat modules have finite flat dimension. In this paper we extend the theory to characterize when products of modules in $\\mathcal T$ have finite $\\mathcal T$-projective dimension, where $\\mathcal T$ is the left hand class of a Tor-pair $(\\mathcal T,\\mathcal S)$, relating this property with the relative $\\mathcal T$-Mittag-Leffler dimension of modules in $\\mathcal S$. We apply these results to study the existence of approximations by modules in $\\mathcal T$. In order to do this, we give short proofs of the well known results that a dec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07547","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"}