{"paper":{"title":"Vanishing Properties of Dual Bass numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Lingguang Li","submitted_at":"2010-05-11T08:37:17Z","abstract_excerpt":"Let $R$ be a Noetherian ring, $M$ an Artinian $R$-module, $\\p\\in\\Cos_RM$. Then $\\cograde_{R_{\\p}}\\Hom_{R}(R_{\\p},M)=\\inf\\{i | \\pi_{i}(\\p,M)>0\\}$ and $$\\pi_{i}(\\p,M)>0\\Rightarrow\\cograde_{R_{\\p}}\\Hom_{R}(R_{\\p},M)\\leq i\\leq\\fd_{R_{\\p}}\\Hom_{R}(R_{\\p},M),$$ where $\\pi_{i}(\\p,M)$ is the $i$-th dual Bass number of $M$ with respect to $\\p$, the integer $\\cograde_{R_{\\p}}\\Hom_{R}(R_{\\p},M)$ is the common length of any maximal $\\Hom_{R}(R_{\\p},M)$-quasi co-regular sequence contained in $\\p R_{\\p}$, and $\\fd_{R_{\\p}}\\Hom_{R}(R_{\\p},M)$ is the flat dimension of $R_{\\p}$-module $\\Hom_{R}(R_{\\p},M)$ (The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1754","kind":"arxiv","version":5},"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"}