{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WH3CBDBEUNPYJFGQUIARTWHTCM","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":"77f174353d77d9d2ae5f5fae5d08deb56100298d373030114f0e7a1fd957cbe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-13T17:27:21Z","title_canon_sha256":"02548262c9f1126dfbc7a3ff4e71d71e8293780563c785117dc897e494f25bd1"},"schema_version":"1.0","source":{"id":"1709.04435","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04435","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04435v5","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04435","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"WH3CBDBEUNPY","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WH3CBDBEUNPYJFGQ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WH3CBDBE","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:f689ec63fbce86ec60628cce0ba78c26fbaac6a933d80c22e957155e5b90ac10","target":"graph","created_at":"2026-05-17T23:53:06Z","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 $K$ be a commutative Noetherian ring with identity, let $A$ be a $K$-algebra, and let $B$ be a subalgebra of $A$ such that $A/B$ is finitely generated as a $K$-module. The main result of the paper is that $A$ is finitely presented (resp. finitely generated) if and only if $B$ is finitely presented (resp. finitely generated). As corollaries we obtain: a subring of finite index in a finitely presented ring is finitely presented; a subalgebra of finite co-dimension in a finitely presented algebra over a field is finitely presented (already shown by Voden in 2009). We also discuss the role of ","authors_text":"Nik Ruskuc, Peter Mayr","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-13T17:27:21Z","title":"Presentations for subrings and subalgebras of finite co-rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04435","kind":"arxiv","version":5},"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:ae11b72e390c987b4586f0370e42e09d010958cb04d3ba01cb640a149b063520","target":"record","created_at":"2026-05-17T23:53:06Z","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":"77f174353d77d9d2ae5f5fae5d08deb56100298d373030114f0e7a1fd957cbe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-13T17:27:21Z","title_canon_sha256":"02548262c9f1126dfbc7a3ff4e71d71e8293780563c785117dc897e494f25bd1"},"schema_version":"1.0","source":{"id":"1709.04435","kind":"arxiv","version":5}},"canonical_sha256":"b1f6208c24a35f8494d0a20119d8f3133efc7a7d7e8fe050ea7bc545bfd180b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1f6208c24a35f8494d0a20119d8f3133efc7a7d7e8fe050ea7bc545bfd180b8","first_computed_at":"2026-05-17T23:53:06.784783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:06.784783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NGpEUzCj2dhYG4sQotPGHBgt6dxA/UYpgyP1gSFA19urWixy/nLOlQqMgil16/iqToDyhvbFxa7vfckDALRRBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:06.785409Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04435","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae11b72e390c987b4586f0370e42e09d010958cb04d3ba01cb640a149b063520","sha256:f689ec63fbce86ec60628cce0ba78c26fbaac6a933d80c22e957155e5b90ac10"],"state_sha256":"cda21e409cb5cb7930f3e945503943feda2b7f5efa81c8c30883b2e38ff94d08"}