{"paper":{"title":"Dual of Bass numbers and dualizing modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"A.-J. Taherizadeh, M. Rahmani","submitted_at":"2015-08-24T14:09:33Z","abstract_excerpt":"Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using relative homological dimensions with respect to $C$, we impose various conditions on $C$ to be dualizing. First, we show that $C$ is dualizing if and only if there exists a Cohen-Macaulay $R$-module of type 1 and of finite G$ _C $-dimension. This result extends Takahashi \\cite[Theorem 2.3]{T} as well as Christensen \\cite[Proposition 8.4]{C}. Next, as a generalization of Xu \\cite[Theorem 3.2]{X2}, we show that $C$ is dualizing if and only if for an $R$-module $M$, the necessary and sufficient conditi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05813","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"}