{"paper":{"title":"On bounds of homological dimensions in Nakayama algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dag Oskar Madsen, Rene Marczinzik","submitted_at":"2017-10-12T09:32:39Z","abstract_excerpt":"Let $A$ be a Nakayama algebra with $n$ simple modules and a simple module $S$ of even projective dimension $m$. Choose $m$ minimal such that a simple $A$-module with projective dimension $2m$ exists, then we show that the global dimension of $A$ is bounded by $n+m-1$. This gives a combined generalisation of results of Gustafson \\cite{Gus} and Madsen \\cite{Mad}. In \\cite{Bro}, Brown proved that the global dimension of quasi-hereditary Nakayama algebras with $n$ simple modules is bounded by $n$. Using our result on the bounds of global dimensions of Nakayama algebras, we give a short new proof o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04420","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"}