{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZOSH4YTGV3FGY6UIZTVV3HSKRM","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":"b20754ada4f841d7d2b75d83cdd0a380691385f4b2cfec283d8fc9e92ef3fedc","cross_cats_sorted":["math.NT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-08-29T10:22:57Z","title_canon_sha256":"c91d480c101b4958fa6e4ca597dbdc3d48dca5c9aafa3c8a146b3441fbeffbb8"},"schema_version":"1.0","source":{"id":"1508.07430","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07430","created_at":"2026-05-18T01:34:32Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07430v1","created_at":"2026-05-18T01:34:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07430","created_at":"2026-05-18T01:34:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZOSH4YTGV3FG","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZOSH4YTGV3FGY6UI","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZOSH4YTG","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:c74983225b49e5257ebd3a74b897987262f8502453a8b39c338feb734f214d97","target":"graph","created_at":"2026-05-18T01:34:32Z","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":"In this paper we show that if $I$ is an ideal of a commutative semigroup $C$ such that the separator $SepI$ of $I$ is not empty then the factor semigroup $S=C/P_I$ ($P_I$ is the principal congruence on $C$ defined by $I$) satisfies Condition $(*)$: $S$ is a commutative monoid with a zero; The annihilator $A(s)$ of every non identity element $s$ of $S$ contains a non zero element of $S$; $A(s)=A(t)$ implies $s=t$ for every $s, t\\in S$. Conversely, if $\\alpha$ is a congruence on a commutative semigroup $C$ such that the factor semigroup $S=C/\\alpha$ satisfies Condition $(*)$ then there is an ide","authors_text":"Attila Nagy","cross_cats":["math.NT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-08-29T10:22:57Z","title":"Separators of Ideals in Multiplicative Semigroups of Unique Factorization Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07430","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:edadfacbad3132d6af763a46debabac9e53c0df4b174ff882540679210f849f6","target":"record","created_at":"2026-05-18T01:34:32Z","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":"b20754ada4f841d7d2b75d83cdd0a380691385f4b2cfec283d8fc9e92ef3fedc","cross_cats_sorted":["math.NT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-08-29T10:22:57Z","title_canon_sha256":"c91d480c101b4958fa6e4ca597dbdc3d48dca5c9aafa3c8a146b3441fbeffbb8"},"schema_version":"1.0","source":{"id":"1508.07430","kind":"arxiv","version":1}},"canonical_sha256":"cba47e6266aeca6c7a88cceb5d9e4a8b142375fa37ffb1bac2191aff53f99a30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cba47e6266aeca6c7a88cceb5d9e4a8b142375fa37ffb1bac2191aff53f99a30","first_computed_at":"2026-05-18T01:34:32.320393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:32.320393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tnweLzXsxS3sFU/87A8BO0p3k929e/3VPCLFBol26YjSuHc1FnzPBrSDGxIYYk3bgu6mvDmlzi9xf08zDCdMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:32.321162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07430","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edadfacbad3132d6af763a46debabac9e53c0df4b174ff882540679210f849f6","sha256:c74983225b49e5257ebd3a74b897987262f8502453a8b39c338feb734f214d97"],"state_sha256":"d9d05b5df2c8348f366df48719496a0c158aebfda64c218c5aea63b8fdd875ed"}