{"paper":{"title":"Linkage of ideals over a module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Khadijeh Sayyari, Maryam Jahangiri","submitted_at":"2017-09-11T07:20:09Z","abstract_excerpt":"Inspired by the works in linkage theory of ideals, we define the concept of linkage of ideals over a module. Several known theorems in linkage theory are improved or recovered by new approaches. Specially, we make some extensions and generalizations of the basic result of Peskine and Szpiro \\cite[prop 1.3]{PS}, namely if $R$ is a Gorenstain local ring, $\\mathfrak{a} \\neq 0$ (an ideal of $R$) and $\\mathfrak{b} := 0:_R \\mathfrak{a}$ then $\\frac{R}{\\mathfrak{a}}$ is Cohen-Macaulay if and only if $\\frac{R}{\\mathfrak{a}}$ is unmixed and $\\frac{R}{\\mathfrak{b}}$ is Cohen-Macaulay."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03268","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"}