{"paper":{"title":"Gorenstein projective dimensions of modules over minimal Auslander-Gorenstein algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Ren\\'e Marczinzik, Shen Li, Shunhua Zhang","submitted_at":"2018-02-01T04:03:33Z","abstract_excerpt":"In this article we investigate the relations between the Gorenstein projective dimensions of $\\Lambda$-modules and their socles for minimal n-Auslander-Gorenstein algebras $\\Lambda$ in the sense of Iyama and Solberg \\cite{IS}. First we give a description of projective-injective $\\Lambda$-modules in terms of their socles. Then we prove that a $\\Lambda$-module $N$ has Gorenstein projective dimension at most n iff its socle has Gorenstein projective dimension at most n iff $N$ is cogenerated by a projective $\\Lambda$-module. Furthermore, we show that minimal n-Auslander-Gorenstein algebras can be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00149","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"}