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This gives an affirmative answer to Problem~9 in \\emph{Open Problems in Commutative Ring Theory}. The construction combines Akiba's Nagata-type example, which already yields an integrally closed reduced ring with integrally closed domain localizations and a finitely generated ideal of zero-divisors with zero annihilator, with an explicit "},"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":"2604.07465","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-04-08T18:04:13Z","cross_cats_sorted":[],"title_canon_sha256":"a20da02a7b87dedf5975477564367c556f157d22afba6299c0a2c309646b1f55","abstract_canon_sha256":"66662ea7ca194d1124d7ea14317ddd05d9e7dd7f586a543e2a1a293c5f446049"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:04:47.372143Z","signature_b64":"dUWG5jx3Cj3K+HRGcrirxKINCnZ1M0VOTILejijd86OuvDb5UKgAEunkwcDfcBFAxv9/Kez8xkOKKrtlff9mDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1792c992c9c94c2fcb2105c18ba0e91bc5d90a2cafdd96a2d50b6a5a89bf1ed","last_reissued_at":"2026-05-28T02:04:47.371642Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:04:47.371642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Integrally Closed Reduced Ring with McCoy Localizations That Is Neither McCoy nor Locally a Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"There exists a reduced and integrally closed commutative ring whose localizations at all maximal ideals are McCoy rings, but the ring itself is neither McCoy nor locally a domain.","cross_cats":[],"primary_cat":"math.AC","authors_text":"Haotian Ma","submitted_at":"2026-04-08T18:04:13Z","abstract_excerpt":"We construct an explicit commutative ring $R$ that is reduced and integrally closed, such that $R_{\\mathfrak p}$ is an integrally closed McCoy ring for every maximal ideal $\\mathfrak p$ of $R$, while $R$ itself is not a McCoy ring and is not locally a domain. This gives an affirmative answer to Problem~9 in \\emph{Open Problems in Commutative Ring Theory}. 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