{"paper":{"title":"Homological behavior of Auslander's $k$-Gorenstein rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Hourong Qin, Zhaoyong Huang","submitted_at":"2004-09-09T13:42:24Z","abstract_excerpt":"In this paper we mainly study the homological properties of dual modules over $k$-Gorenstein rings. For a right quasi $k$-Gorenstein ring $\\Lambda$, we show that the right self-injective dimension of $\\Lambda$ is at most $k$ if and only if each $M \\in$mod $\\Lambda$ satisfying the condition that Ext$_{\\Lambda}^i(M, \\Lambda)=0$ for any $1\\leq i \\leq k$ is reflexive. For an $\\infty$-Gorenstein ring, we show that the big and small finitistic dimensions and the self-injective dimension of $\\Lambda$ are identical. In addition, we show that if $\\Lambda$ is a left quasi $\\infty$-Gorenstein ring and $M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409161","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"}