{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FB4NV5XOBVJKSOX5WAARZ33MAH","short_pith_number":"pith:FB4NV5XO","schema_version":"1.0","canonical_sha256":"2878daf6ee0d52a93afdb0011cef6c01cec1ec2473dbdb356d5a8616af0d5620","source":{"kind":"arxiv","id":"1607.05341","version":1},"attestation_state":"computed","paper":{"title":"A note on Itoh (e)-Valuation Rings of and Ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David E. Rush, Louis J. Ratliff, Youngsu Kim","submitted_at":"2016-07-18T22:31:04Z","abstract_excerpt":"Let $I$ be a regular proper ideal in a Noetherian ring $R$, let $e \\ge 2$ be an integer, let $\\mathbf T_e = R[u,tI,u^{\\frac{1}{e}}]' \\cap R[u^{\\frac{1}{e}},t^{\\frac{1}{e}}]$ (where $t$ is an indeterminate and $u =\\frac{1}{t}$), and let $\\mathbf r_e = u^{\\frac{1}{e}} \\mathbf T_e$. Then the Itoh (e)-valuation rings of $I$ are the rings $(\\mathbf T_e/z)_{(p/z)}$, where $p$ varies over the (height one) associated prime ideals of $\\mathbf r_e$ and $z$ is the (unique) minimal prime ideal in $\\mathbf T_e$ that is contained in $p$. We show, among other things:\n  (1) $\\mathbf r_e$ is a radical ideal if"},"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":"1607.05341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-07-18T22:31:04Z","cross_cats_sorted":[],"title_canon_sha256":"e79a6c7bad1001018e7fee266d7ea0b72e483b40578197b87739124d2b37d5a7","abstract_canon_sha256":"e81a1e5df701eaf8152a350de6221e1106dfc1908a63e785752c8753e32ddf8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:55.201747Z","signature_b64":"onaazdXMsk4+ukVkpDryFQWbALV7AcBk1y1e0FC9bIZDCv3tvX17WAOAGYxjo+nPYBjJ8YCq/PlK4+wshwLHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2878daf6ee0d52a93afdb0011cef6c01cec1ec2473dbdb356d5a8616af0d5620","last_reissued_at":"2026-05-18T01:10:55.201287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:55.201287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on Itoh (e)-Valuation Rings of and Ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David E. Rush, Louis J. Ratliff, Youngsu Kim","submitted_at":"2016-07-18T22:31:04Z","abstract_excerpt":"Let $I$ be a regular proper ideal in a Noetherian ring $R$, let $e \\ge 2$ be an integer, let $\\mathbf T_e = R[u,tI,u^{\\frac{1}{e}}]' \\cap R[u^{\\frac{1}{e}},t^{\\frac{1}{e}}]$ (where $t$ is an indeterminate and $u =\\frac{1}{t}$), and let $\\mathbf r_e = u^{\\frac{1}{e}} \\mathbf T_e$. Then the Itoh (e)-valuation rings of $I$ are the rings $(\\mathbf T_e/z)_{(p/z)}$, where $p$ varies over the (height one) associated prime ideals of $\\mathbf r_e$ and $z$ is the (unique) minimal prime ideal in $\\mathbf T_e$ that is contained in $p$. We show, among other things:\n  (1) $\\mathbf r_e$ is a radical ideal if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05341","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":"1607.05341","created_at":"2026-05-18T01:10:55.201364+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.05341v1","created_at":"2026-05-18T01:10:55.201364+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05341","created_at":"2026-05-18T01:10:55.201364+00:00"},{"alias_kind":"pith_short_12","alias_value":"FB4NV5XOBVJK","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FB4NV5XOBVJKSOX5","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FB4NV5XO","created_at":"2026-05-18T12:30:15.759754+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/FB4NV5XOBVJKSOX5WAARZ33MAH","json":"https://pith.science/pith/FB4NV5XOBVJKSOX5WAARZ33MAH.json","graph_json":"https://pith.science/api/pith-number/FB4NV5XOBVJKSOX5WAARZ33MAH/graph.json","events_json":"https://pith.science/api/pith-number/FB4NV5XOBVJKSOX5WAARZ33MAH/events.json","paper":"https://pith.science/paper/FB4NV5XO"},"agent_actions":{"view_html":"https://pith.science/pith/FB4NV5XOBVJKSOX5WAARZ33MAH","download_json":"https://pith.science/pith/FB4NV5XOBVJKSOX5WAARZ33MAH.json","view_paper":"https://pith.science/paper/FB4NV5XO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.05341&json=true","fetch_graph":"https://pith.science/api/pith-number/FB4NV5XOBVJKSOX5WAARZ33MAH/graph.json","fetch_events":"https://pith.science/api/pith-number/FB4NV5XOBVJKSOX5WAARZ33MAH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FB4NV5XOBVJKSOX5WAARZ33MAH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FB4NV5XOBVJKSOX5WAARZ33MAH/action/storage_attestation","attest_author":"https://pith.science/pith/FB4NV5XOBVJKSOX5WAARZ33MAH/action/author_attestation","sign_citation":"https://pith.science/pith/FB4NV5XOBVJKSOX5WAARZ33MAH/action/citation_signature","submit_replication":"https://pith.science/pith/FB4NV5XOBVJKSOX5WAARZ33MAH/action/replication_record"}},"created_at":"2026-05-18T01:10:55.201364+00:00","updated_at":"2026-05-18T01:10:55.201364+00:00"}