{"paper":{"title":"On the relative Cohen-Macaulay modules","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Majid Rahro Zargar","submitted_at":"2013-03-09T13:35:21Z","abstract_excerpt":"Let $R$ be a commutative Noetherian local ring and let $\\fa$ be a proper ideal of $R$. A non-zero finitely generated $R$-module $M$ is called relative Cohen-Macaulay with respect to $\\fa$ if there is precisely one non vanishing local cohomology modules $\\H_{\\fa}^{i}(M)$ of $M$. In this paper, as a main result, it is shown that if $M$ is a Gorenstein $R$--module, then $\\H_{\\fa}^{i}(M)=0$ for all $i\\neq c$ where $c=\\h_{M}\\fa$ is completely encoded in homological properties of $\\H_{\\fa}^{c}(M)$, in particular in its Bass numbers. Notice that, this result provides a generalization of a result of M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2208","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"}