{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6OUOJMV2NZDGWSQZVSDIJMDMSH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6b702e1a7a0e27c12fe1ea14b87499ae84be03ca93ed577f700d396642bf9b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-09-11T07:20:09Z","title_canon_sha256":"32f2db796b811e5f357b60e49703b9a971870153ef0c2d75baae6bd90f768cb0"},"schema_version":"1.0","source":{"id":"1709.03268","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03268","created_at":"2026-05-18T00:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03268v3","created_at":"2026-05-18T00:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03268","created_at":"2026-05-18T00:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"6OUOJMV2NZDG","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6OUOJMV2NZDGWSQZ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6OUOJMV2","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:61ddadba2d832542e818f30fe49dcbf390c43a67576c842deb28452aacd4fa0e","target":"graph","created_at":"2026-05-18T00:03:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Inspired by the works in linkage theory of ideals, we define the concept of linkage of ideals over a module. Several known theorems in linkage theory are improved or recovered by new approaches. Specially, we make some extensions and generalizations of the basic result of Peskine and Szpiro \\cite[prop 1.3]{PS}, namely if $R$ is a Gorenstain local ring, $\\mathfrak{a} \\neq 0$ (an ideal of $R$) and $\\mathfrak{b} := 0:_R \\mathfrak{a}$ then $\\frac{R}{\\mathfrak{a}}$ is Cohen-Macaulay if and only if $\\frac{R}{\\mathfrak{a}}$ is unmixed and $\\frac{R}{\\mathfrak{b}}$ is Cohen-Macaulay.","authors_text":"Khadijeh Sayyari, Maryam Jahangiri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-09-11T07:20:09Z","title":"Linkage of ideals over a module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03268","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5a585dad3ef46ab11a45c7f6c92e87c0fc5a0e70b8ddab53e8c849ec9fc9add3","target":"record","created_at":"2026-05-18T00:03:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6b702e1a7a0e27c12fe1ea14b87499ae84be03ca93ed577f700d396642bf9b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-09-11T07:20:09Z","title_canon_sha256":"32f2db796b811e5f357b60e49703b9a971870153ef0c2d75baae6bd90f768cb0"},"schema_version":"1.0","source":{"id":"1709.03268","kind":"arxiv","version":3}},"canonical_sha256":"f3a8e4b2ba6e466b4a19ac8684b06c91f6ad8fb0e735b4988baba4af963b645b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3a8e4b2ba6e466b4a19ac8684b06c91f6ad8fb0e735b4988baba4af963b645b","first_computed_at":"2026-05-18T00:03:19.498656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:19.498656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uXfPJ7pbMbgT7Dr++gEwMNOn76qS6hUyzpn/iliOfTvmF44F8QdciH5NQptbJPpXtSPP9RI4TzSkJKwy5/TECA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:19.499150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03268","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a585dad3ef46ab11a45c7f6c92e87c0fc5a0e70b8ddab53e8c849ec9fc9add3","sha256:61ddadba2d832542e818f30fe49dcbf390c43a67576c842deb28452aacd4fa0e"],"state_sha256":"a26cdfcb77c67ebbe539800235ea21f5c4e62c4cb1f9c0add83055af779048ae"}