{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PW7JAP2R2XKIXXN2XKAE4FL5FF","short_pith_number":"pith:PW7JAP2R","schema_version":"1.0","canonical_sha256":"7dbe903f51d5d48bddbaba804e157d29681ae73f8f73b6dc8ee1eaecfa9e6053","source":{"kind":"arxiv","id":"1901.06304","version":1},"attestation_state":"computed","paper":{"title":"Divisibility Theory of Commutative Rings and Ideal Distributivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Agnes Szendrei, Keith A. Kearnes, P. N. Anh","submitted_at":"2019-01-18T15:48:26Z","abstract_excerpt":"We begin by investigating the class of commutative unital rings in which no two distinct elements divide the same elements. We prove that this class forms a finitely axiomatizable, relatively ideal distributive quasivariety, and it equals the quasivariety generated by the class of integral domains with trivial unit group. We end the paper by proving a representation theorem that provides more evidence to the conjecture that B\\'ezout monoids describe exactly the monoids of finitely generated ideals of commutative unital rings with distributive ideal lattice."},"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":"1901.06304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-18T15:48:26Z","cross_cats_sorted":[],"title_canon_sha256":"ac62b9d54e85b14c4fff2ea277d532ea5d734dac82d533ca26fe47a378ef58da","abstract_canon_sha256":"3b846b2129dfdcaf0dc228b7df76b137b3749eb8ee065fffded22f6ad5761c8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:01.424811Z","signature_b64":"g/d2VkV6PTy9l/4VM9PLEPjEUyZSfuj3U9wEy88XSqr+jq6e/OkyWTH5m+oqr7OOGbdrCOHVFQHMCCyOriFnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dbe903f51d5d48bddbaba804e157d29681ae73f8f73b6dc8ee1eaecfa9e6053","last_reissued_at":"2026-05-17T23:56:01.424170Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:01.424170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Divisibility Theory of Commutative Rings and Ideal Distributivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Agnes Szendrei, Keith A. Kearnes, P. N. Anh","submitted_at":"2019-01-18T15:48:26Z","abstract_excerpt":"We begin by investigating the class of commutative unital rings in which no two distinct elements divide the same elements. We prove that this class forms a finitely axiomatizable, relatively ideal distributive quasivariety, and it equals the quasivariety generated by the class of integral domains with trivial unit group. We end the paper by proving a representation theorem that provides more evidence to the conjecture that B\\'ezout monoids describe exactly the monoids of finitely generated ideals of commutative unital rings with distributive ideal lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06304","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":"1901.06304","created_at":"2026-05-17T23:56:01.424265+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.06304v1","created_at":"2026-05-17T23:56:01.424265+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.06304","created_at":"2026-05-17T23:56:01.424265+00:00"},{"alias_kind":"pith_short_12","alias_value":"PW7JAP2R2XKI","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"PW7JAP2R2XKIXXN2","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"PW7JAP2R","created_at":"2026-05-18T12:33:24.271573+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/PW7JAP2R2XKIXXN2XKAE4FL5FF","json":"https://pith.science/pith/PW7JAP2R2XKIXXN2XKAE4FL5FF.json","graph_json":"https://pith.science/api/pith-number/PW7JAP2R2XKIXXN2XKAE4FL5FF/graph.json","events_json":"https://pith.science/api/pith-number/PW7JAP2R2XKIXXN2XKAE4FL5FF/events.json","paper":"https://pith.science/paper/PW7JAP2R"},"agent_actions":{"view_html":"https://pith.science/pith/PW7JAP2R2XKIXXN2XKAE4FL5FF","download_json":"https://pith.science/pith/PW7JAP2R2XKIXXN2XKAE4FL5FF.json","view_paper":"https://pith.science/paper/PW7JAP2R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.06304&json=true","fetch_graph":"https://pith.science/api/pith-number/PW7JAP2R2XKIXXN2XKAE4FL5FF/graph.json","fetch_events":"https://pith.science/api/pith-number/PW7JAP2R2XKIXXN2XKAE4FL5FF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PW7JAP2R2XKIXXN2XKAE4FL5FF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PW7JAP2R2XKIXXN2XKAE4FL5FF/action/storage_attestation","attest_author":"https://pith.science/pith/PW7JAP2R2XKIXXN2XKAE4FL5FF/action/author_attestation","sign_citation":"https://pith.science/pith/PW7JAP2R2XKIXXN2XKAE4FL5FF/action/citation_signature","submit_replication":"https://pith.science/pith/PW7JAP2R2XKIXXN2XKAE4FL5FF/action/replication_record"}},"created_at":"2026-05-17T23:56:01.424265+00:00","updated_at":"2026-05-17T23:56:01.424265+00:00"}