{"paper":{"title":"Finite cycles of indecomposable modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrzej Skowro\\'nski, Jos\\'e Antonio de la Pe\\~na, Piotr Malicki","submitted_at":"2013-06-04T21:23:40Z","abstract_excerpt":"We solve a long standing open problem concerning the structure of finite cycles in the category mod A of finitely generated modules over an arbitrary artin algebra A, that is, the chains of homomorphisms $M_0 \\stackrel{f_1}{\\rightarrow} M_1 \\to \\cdots \\to M_{r-1} \\stackrel{f_r}{\\rightarrow} M_r=M_0$ between indecomposable modules in mod A which do not belong to the infinite radical of mod A. In particular, we describe completely the structure of an arbitrary module category mod A whose all cycles are finite. The main structural results of the paper allow to derive several interesting combinato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0929","kind":"arxiv","version":2},"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"}