{"paper":{"title":"The finiteness dimension of modules and relative Cohen-Macaulayness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kh. Ahmadi Amoli, M. Mast Zohouri","submitted_at":"2017-02-01T09:40:16Z","abstract_excerpt":"Let $R$ be a commutative Noetherian ring, $\\mathfrak a$ and $\\mathfrak b$ ideals of $R$. In this paper, we study the finiteness dimension $f_{\\mathfrak a}(M)$ of $M$ relative to $\\mathfrak a$ and the $\\mathfrak b$-minimum $\\mathfrak a$-adjusted depth $\\lambda_{\\mathfrak a}^{\\mathfrak b}(M)$ of $M$, where the underlying module $M$ is relative Cohen-Macaulay w.r.t $\\mathfrak a$. Some applications of such modules are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00175","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"}