{"paper":{"title":"A Few Comments On Matlis Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Waqas Mahmood","submitted_at":"2013-11-07T04:43:59Z","abstract_excerpt":"For a Noetherian local ring $(R,{\\mathfrak m})$ with $\\mathfrak p\\in \\Spec(R)$ we denote $E_R(R/\\mathfrak p)$ by the $R$-injective hull of $R/\\mathfrak p$. We will show that it has an $\\hat{R}^\\mathfrak p$-module structure and there is an isomorphism $E_R(R/\\mathfrak p)\\cong E_{\\hat{R}^\\mathfrak p}(\\hat{R}^\\mathfrak p/\\mathfrak p\\hat{R}^\\mathfrak p)$ where $\\hat{R}^\\mathfrak p$ stands for the $\\mathfrak p$-adic completion of $R$. Moreover for a complete Cohen-Macaulay ring $R$ the module $D(E_R(R/\\mathfrak p))$ is isomorphic to $\\hat{R}_\\mathfrak{p}$ provided that $\\dim(R/\\mathfrak p)=1$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1573","kind":"arxiv","version":1},"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"}