{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:IF4TKKVNU6LOQ32TY3XUCSWG6E","short_pith_number":"pith:IF4TKKVN","schema_version":"1.0","canonical_sha256":"4179352aada796e86f53c6ef414ac6f1280c40e89154d79cc0bc377f1adf8b0c","source":{"kind":"arxiv","id":"1906.11138","version":1},"attestation_state":"computed","paper":{"title":"On the atomicity of monoid algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Felix Gotti, Jim Coykendall","submitted_at":"2019-06-26T14:54:42Z","abstract_excerpt":"Let $M$ be a commutative cancellative monoid, and let $R$ be an integral domain. The question of whether the monoid ring $R[x;M]$ is atomic provided that both $M$ and $R$ are atomic dates back to the 1980s. In 1993, Roitman gave a negative answer to the question for $M = \\mathbb{N}_0$: he constructed an atomic integral domain $R$ such that the polynomial ring $R[x]$ is not atomic. However, the question of whether a monoid algebra $F[x;M]$ over a field $F$ is atomic provided that $M$ is atomic has been open since then. Here we offer a negative answer to this question. First, we find for any inf"},"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":"1906.11138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-26T14:54:42Z","cross_cats_sorted":[],"title_canon_sha256":"9a673332d07c5f54f345dc541fb1f549089bd47749b573741369a7405d602c40","abstract_canon_sha256":"607c9430f1e53b0b10f7cf3005fb66c9452b5d243fb07180fa2825159c46fe8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:09.724423Z","signature_b64":"lC/+Iv4QAFI48JBc04KZNxvUY2lt5lNcuefasKJNN32WN7WCqe/na2m+h29m3jsVVlpd+PnurOSSjrFV84cnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4179352aada796e86f53c6ef414ac6f1280c40e89154d79cc0bc377f1adf8b0c","last_reissued_at":"2026-05-17T23:42:09.723725Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:09.723725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the atomicity of monoid algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Felix Gotti, Jim Coykendall","submitted_at":"2019-06-26T14:54:42Z","abstract_excerpt":"Let $M$ be a commutative cancellative monoid, and let $R$ be an integral domain. The question of whether the monoid ring $R[x;M]$ is atomic provided that both $M$ and $R$ are atomic dates back to the 1980s. In 1993, Roitman gave a negative answer to the question for $M = \\mathbb{N}_0$: he constructed an atomic integral domain $R$ such that the polynomial ring $R[x]$ is not atomic. However, the question of whether a monoid algebra $F[x;M]$ over a field $F$ is atomic provided that $M$ is atomic has been open since then. Here we offer a negative answer to this question. First, we find for any inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11138","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":"1906.11138","created_at":"2026-05-17T23:42:09.723831+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.11138v1","created_at":"2026-05-17T23:42:09.723831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11138","created_at":"2026-05-17T23:42:09.723831+00:00"},{"alias_kind":"pith_short_12","alias_value":"IF4TKKVNU6LO","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"IF4TKKVNU6LOQ32T","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"IF4TKKVN","created_at":"2026-05-18T12:33:18.533446+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/IF4TKKVNU6LOQ32TY3XUCSWG6E","json":"https://pith.science/pith/IF4TKKVNU6LOQ32TY3XUCSWG6E.json","graph_json":"https://pith.science/api/pith-number/IF4TKKVNU6LOQ32TY3XUCSWG6E/graph.json","events_json":"https://pith.science/api/pith-number/IF4TKKVNU6LOQ32TY3XUCSWG6E/events.json","paper":"https://pith.science/paper/IF4TKKVN"},"agent_actions":{"view_html":"https://pith.science/pith/IF4TKKVNU6LOQ32TY3XUCSWG6E","download_json":"https://pith.science/pith/IF4TKKVNU6LOQ32TY3XUCSWG6E.json","view_paper":"https://pith.science/paper/IF4TKKVN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.11138&json=true","fetch_graph":"https://pith.science/api/pith-number/IF4TKKVNU6LOQ32TY3XUCSWG6E/graph.json","fetch_events":"https://pith.science/api/pith-number/IF4TKKVNU6LOQ32TY3XUCSWG6E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IF4TKKVNU6LOQ32TY3XUCSWG6E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IF4TKKVNU6LOQ32TY3XUCSWG6E/action/storage_attestation","attest_author":"https://pith.science/pith/IF4TKKVNU6LOQ32TY3XUCSWG6E/action/author_attestation","sign_citation":"https://pith.science/pith/IF4TKKVNU6LOQ32TY3XUCSWG6E/action/citation_signature","submit_replication":"https://pith.science/pith/IF4TKKVNU6LOQ32TY3XUCSWG6E/action/replication_record"}},"created_at":"2026-05-17T23:42:09.723831+00:00","updated_at":"2026-05-17T23:42:09.723831+00:00"}