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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 $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1311.1573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-11-07T04:43:59Z","cross_cats_sorted":[],"title_canon_sha256":"9030ce68cd6b42123d18cd0575b9f790ad6c5e7cf9aebefa18072bf733750aae","abstract_canon_sha256":"61d45e05a3dad886878411ceb9bd2fbd6be594093b9dd1ba55cc9ca9bf53211f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:43.835692Z","signature_b64":"KTyoweOIvg8AhXMGMy67vwqf1oKlsyDuFOjCKaQr9XeRntvNFRjlonErC2/Z9eOnH0PsTMl6AN4B5cTgTM0VBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fab921729e5925bc8a7713fa46d43976f2eeef6c0125c28c9d596567cd408a36","last_reissued_at":"2026-05-18T03:07:43.835172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:43.835172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $R/\\mathfrak p$. 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