{"paper":{"title":"Excellent extensions and homological conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Yingying Zhang","submitted_at":"2017-02-20T09:01:20Z","abstract_excerpt":"In this paper, we introduce the notion of excellent extension of rings. Let $\\Gamma$ be an excellent extension of an artin algebra $\\Lambda$, we prove that $\\Lambda$ satisfies the Gorenstein symmetry conjecture (resp. finitistic dimension conjecture, Auslander-Gorenstein conjecture, Nakayama conjecture) if and only if so does $\\Gamma$. As a special case of excellent extensions, if $G$ is a finite group whose order is invertible in $\\Lambda$ acting on $\\Lambda$ and $\\Lambda$ is $G$-stable, we prove that if the skew group algebras $\\Lambda G$ satisfies strong Nakayama conjecture (resp. generaliz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05902","kind":"arxiv","version":3},"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"}