{"paper":{"title":"A ring theoretic approach to the finite representation type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Rasool Hafezi","submitted_at":"2018-05-23T11:23:00Z","abstract_excerpt":"An Artin algebra $\\Lambda$ is said to be of finite Cohen-Macaulay type, $\\rm{CM}$-finite for short, if the full subcategory $\\rm{Gprj}\\mbox{-} \\Lambda$ of finitely generated Gorenstein projective $\\Lambda$-modules is of finite representation type. If $\\Lambda$ is a $\\rm{CM}$-finite algebra, then we denote by $\\rm{Aus}(\\underline{\\rm{Gprj}}\\mbox{-} \\Lambda)$ the stable Cohen-Macaulay Auslander algebra, i.e. $\\rm{\\underline{End}}_{\\Lambda}(G)$, where $G $ is a basic representation generator of $\\rm{Gprj}\\mbox{-}\\Lambda$. In this paper, we will explain how by defining an equivalence relation on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09062","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":""},"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"}