{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:26ETNWIA2BUAUYYR4YYDHXCAFU","short_pith_number":"pith:26ETNWIA","schema_version":"1.0","canonical_sha256":"d78936d900d0680a6311e63033dc402d009682c61e66762377781bd868156c49","source":{"kind":"arxiv","id":"1501.03126","version":1},"attestation_state":"computed","paper":{"title":"On Cohen-Macaulayness and depth of ideals in invariant rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Martin Kohls, M\\\"ufit Sezer","submitted_at":"2015-01-13T19:38:12Z","abstract_excerpt":"We investigate the presence of Cohen-Macaulay ideals in invariant rings and show that an ideal of an invariant ring corresponding to a modular representation of a $p$-group is not Cohen-Macaulay unless the invariant ring itself is. As an intermediate result, we obtain that non-Cohen-Macaulay factorial rings cannot contain Cohen-Macaulay ideals. For modular cyclic groups of prime order, we show that the quotient of the invariant ring modulo the transfer ideal is always Cohen-Macaulay, extending a result of Fleischmann."},"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":"1501.03126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-01-13T19:38:12Z","cross_cats_sorted":[],"title_canon_sha256":"99911ab2e7b5c1c1a3d1e882d6f9a1aa053c270bd2d0d3202c6ca0660de69387","abstract_canon_sha256":"f89eeb7a668a0bc91b2b5d357230f71148383c62a296d5e63ddc67d79e5c93a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:16.687893Z","signature_b64":"pbEuU0AB2wL82PdudweGM2dMYPxtJRdAg9i6/hjpC9JWIbpDDleOeS21zCFYgdJnBD7YPpA0sbCCFC5TObQFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d78936d900d0680a6311e63033dc402d009682c61e66762377781bd868156c49","last_reissued_at":"2026-05-18T01:23:16.687140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:16.687140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Cohen-Macaulayness and depth of ideals in invariant rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Martin Kohls, M\\\"ufit Sezer","submitted_at":"2015-01-13T19:38:12Z","abstract_excerpt":"We investigate the presence of Cohen-Macaulay ideals in invariant rings and show that an ideal of an invariant ring corresponding to a modular representation of a $p$-group is not Cohen-Macaulay unless the invariant ring itself is. As an intermediate result, we obtain that non-Cohen-Macaulay factorial rings cannot contain Cohen-Macaulay ideals. For modular cyclic groups of prime order, we show that the quotient of the invariant ring modulo the transfer ideal is always Cohen-Macaulay, extending a result of Fleischmann."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03126","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":"1501.03126","created_at":"2026-05-18T01:23:16.687267+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.03126v1","created_at":"2026-05-18T01:23:16.687267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03126","created_at":"2026-05-18T01:23:16.687267+00:00"},{"alias_kind":"pith_short_12","alias_value":"26ETNWIA2BUA","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"26ETNWIA2BUAUYYR","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"26ETNWIA","created_at":"2026-05-18T12:28:59.999130+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/26ETNWIA2BUAUYYR4YYDHXCAFU","json":"https://pith.science/pith/26ETNWIA2BUAUYYR4YYDHXCAFU.json","graph_json":"https://pith.science/api/pith-number/26ETNWIA2BUAUYYR4YYDHXCAFU/graph.json","events_json":"https://pith.science/api/pith-number/26ETNWIA2BUAUYYR4YYDHXCAFU/events.json","paper":"https://pith.science/paper/26ETNWIA"},"agent_actions":{"view_html":"https://pith.science/pith/26ETNWIA2BUAUYYR4YYDHXCAFU","download_json":"https://pith.science/pith/26ETNWIA2BUAUYYR4YYDHXCAFU.json","view_paper":"https://pith.science/paper/26ETNWIA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.03126&json=true","fetch_graph":"https://pith.science/api/pith-number/26ETNWIA2BUAUYYR4YYDHXCAFU/graph.json","fetch_events":"https://pith.science/api/pith-number/26ETNWIA2BUAUYYR4YYDHXCAFU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26ETNWIA2BUAUYYR4YYDHXCAFU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26ETNWIA2BUAUYYR4YYDHXCAFU/action/storage_attestation","attest_author":"https://pith.science/pith/26ETNWIA2BUAUYYR4YYDHXCAFU/action/author_attestation","sign_citation":"https://pith.science/pith/26ETNWIA2BUAUYYR4YYDHXCAFU/action/citation_signature","submit_replication":"https://pith.science/pith/26ETNWIA2BUAUYYR4YYDHXCAFU/action/replication_record"}},"created_at":"2026-05-18T01:23:16.687267+00:00","updated_at":"2026-05-18T01:23:16.687267+00:00"}