{"paper":{"title":"Self-orthogonal tau-tilting modules and tilting modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Xiaojin Zhang","submitted_at":"2019-11-18T14:46:44Z","abstract_excerpt":"Let $\\Lambda $ be an artin algebra and $T$ a $\\tau$-tilting $\\Lambda$-module. We prove that $T$ is a tilting module if and only if ${\\rm Ext}_{\\Lambda}^{i}(T,\\Fac T)=0$ for all $i\\geq 1$, where $\\Fac T$ is the full subcategory consisting of modules generated by $T$. Consequently, a $\\tau$-tilting module $T$ of finite projective dimension is a tilting module if and only if ${\\rm Ext}_{\\Lambda}^{i}(T, T)=0$ for all $i\\geq 1$. Moreover, we also give an example to show that a support $\\tau$-tilting but not $\\tau$-tilting module $M$ of finite projective dimension satisfying ${\\rm Ext}_{\\Lambda}^{i}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.07667","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.07667/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}