{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:F6NDX676PCCDNB2EX2ZYN655PA","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":"5f76ee7638f6045520d6d7c5b24d15b6221c8239375e5f803e1ebf80673ba82e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-11-11T21:13:45Z","title_canon_sha256":"f1eff581b343799be0545bad140168dfc0db6b061573ddcf146136f99c2ee3f2"},"schema_version":"1.0","source":{"id":"1711.04197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04197","created_at":"2026-05-18T00:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04197v1","created_at":"2026-05-18T00:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04197","created_at":"2026-05-18T00:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"F6NDX676PCCD","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F6NDX676PCCDNB2E","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F6NDX676","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:35f0fd955fb29637a5c4e10843239e50437f64d19a54d743b443534b92d23a58","target":"graph","created_at":"2026-05-18T00:30:39Z","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":"Let $H$ be a semisimple Hopf algebra, and let $R$ be a noetherian left $H$-module algebra. If $R/R^H$ is a right $H^*$-dense Galois extension, then the invariant subalgebra $R^H$ will inherit the AS-Cohen-Macaulay property from $R$ under some mild conditions, and $R$, when viewed as a right $R^H$-module, is a Cohen-Macaulay module. In particular, we show that if $R$ is a noetherian complete semilocal algebra which is AS-regular of global dimension 2 and $H=\\operatorname{\\bf k} G$ for some finite subgroup $G\\subseteq Aut(R)$, then all the indecomposable Cohen-Macaulay module of $R^H$ is a direc","authors_text":"Jiwei He, Yinhuo Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-11-11T21:13:45Z","title":"Cohen-Macaulay invariant subalgebras of Hopf dense Galois extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04197","kind":"arxiv","version":1},"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:b68661bfb74119b8a98b134e81c3fd9d6d5b9182135719a6061264f1ff040bad","target":"record","created_at":"2026-05-18T00:30:39Z","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":"5f76ee7638f6045520d6d7c5b24d15b6221c8239375e5f803e1ebf80673ba82e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-11-11T21:13:45Z","title_canon_sha256":"f1eff581b343799be0545bad140168dfc0db6b061573ddcf146136f99c2ee3f2"},"schema_version":"1.0","source":{"id":"1711.04197","kind":"arxiv","version":1}},"canonical_sha256":"2f9a3bfbfe7884368744beb386fbbd78183951532b0cc5b00968ec77dc37054b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f9a3bfbfe7884368744beb386fbbd78183951532b0cc5b00968ec77dc37054b","first_computed_at":"2026-05-18T00:30:39.794307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:39.794307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oeadPH2L4YQk+l0doGwSEZWx+pzw4cNeJPbNB3CCNLFqv54ejh/u61zP9WY46i57sJ7b3fWqwXwzTYQx4kivAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:39.795039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04197","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b68661bfb74119b8a98b134e81c3fd9d6d5b9182135719a6061264f1ff040bad","sha256:35f0fd955fb29637a5c4e10843239e50437f64d19a54d743b443534b92d23a58"],"state_sha256":"6d5c1e670bc627da733ca8ff4244f2c838dc75c2eb1a92e743a7c7c890eb3c3d"}