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As the main result we prove that the Matlis dual $\\Hom_R(E_R(R/\\mathfrak{p}), E)$ is isomorphic to $\\hat{R_{\\mathfrak{p}}}$, the completion of $R_{\\mathfrak{p}}$, if and only if $R/\\mathfrak{p}$ is complete. In the case of $R$ a one dimensional domain there is a complete description of $Q \\otimes_R \\hat{R}$ in terms of the com"},"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":"1306.3311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-06-14T07:09:52Z","cross_cats_sorted":[],"title_canon_sha256":"625bf22b7771178d925a53fe3385657f0a2f888732e760290824cddabc0114f3","abstract_canon_sha256":"6edddd8383414c64c5d0dce2d8209af6fc09e121cba408e531896c3c493939dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:57.870703Z","signature_b64":"Vg4AreRN+waVkAWyheiR0pAkHhOSUjpix9CtzV9hBSxWrtu4QDJh06/d/hWRDlFa8l5VQeqXpisHXbSyE/VJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28f71ea3826145782008ba0ef54a14ddca35c2f138dab0c7e6b8499dd37bc742","last_reissued_at":"2026-05-18T03:20:57.870075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:57.870075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the Matlis dual of a certain injective hull","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Peter Schenzel","submitted_at":"2013-06-14T07:09:52Z","abstract_excerpt":"Let $(R,\\mathfrak{m})$ denote a local ring with $E = E_R(R/\\mathfrak{m})$ the injective hull of the residue field. Let $\\mathfrak{p} \\in \\Spec R$ denote a prime ideal with $\\dim R/\\mathfrak{p} = 1$, and let $E_R(R/\\mathfrak{p})$ be the injective hull of $R/\\mathfrak{p}$. As the main result we prove that the Matlis dual $\\Hom_R(E_R(R/\\mathfrak{p}), E)$ is isomorphic to $\\hat{R_{\\mathfrak{p}}}$, the completion of $R_{\\mathfrak{p}}$, if and only if $R/\\mathfrak{p}$ is complete. In the case of $R$ a one dimensional domain there is a complete description of $Q \\otimes_R \\hat{R}$ in terms of the com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3311","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1306.3311","created_at":"2026-05-18T03:20:57.870166+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.3311v1","created_at":"2026-05-18T03:20:57.870166+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3311","created_at":"2026-05-18T03:20:57.870166+00:00"},{"alias_kind":"pith_short_12","alias_value":"FD3R5I4CMFCX","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FD3R5I4CMFCXQIAI","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FD3R5I4C","created_at":"2026-05-18T12:27:45.050594+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FD3R5I4CMFCXQIAIXIHPKSQU3X","json":"https://pith.science/pith/FD3R5I4CMFCXQIAIXIHPKSQU3X.json","graph_json":"https://pith.science/api/pith-number/FD3R5I4CMFCXQIAIXIHPKSQU3X/graph.json","events_json":"https://pith.science/api/pith-number/FD3R5I4CMFCXQIAIXIHPKSQU3X/events.json","paper":"https://pith.science/paper/FD3R5I4C"},"agent_actions":{"view_html":"https://pith.science/pith/FD3R5I4CMFCXQIAIXIHPKSQU3X","download_json":"https://pith.science/pith/FD3R5I4CMFCXQIAIXIHPKSQU3X.json","view_paper":"https://pith.science/paper/FD3R5I4C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.3311&json=true","fetch_graph":"https://pith.science/api/pith-number/FD3R5I4CMFCXQIAIXIHPKSQU3X/graph.json","fetch_events":"https://pith.science/api/pith-number/FD3R5I4CMFCXQIAIXIHPKSQU3X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FD3R5I4CMFCXQIAIXIHPKSQU3X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FD3R5I4CMFCXQIAIXIHPKSQU3X/action/storage_attestation","attest_author":"https://pith.science/pith/FD3R5I4CMFCXQIAIXIHPKSQU3X/action/author_attestation","sign_citation":"https://pith.science/pith/FD3R5I4CMFCXQIAIXIHPKSQU3X/action/citation_signature","submit_replication":"https://pith.science/pith/FD3R5I4CMFCXQIAIXIHPKSQU3X/action/replication_record"}},"created_at":"2026-05-18T03:20:57.870166+00:00","updated_at":"2026-05-18T03:20:57.870166+00:00"}