{"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"}