{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WAVBF4BWFPIQUNE2EUIYQNQGYC","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":"ebadf7119ce7f23af28e263a6b01277203b558424275bbed147626b806968594","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-27T11:41:34Z","title_canon_sha256":"d801f59b193995ac435d63fd92e0140e8c60a6e0e3969985ace92ebb74a5feec"},"schema_version":"1.0","source":{"id":"1012.5598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5598","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5598v1","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5598","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"WAVBF4BWFPIQ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WAVBF4BWFPIQUNE2","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WAVBF4BW","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:0ddda43de96af483fd26814fce723f30b9fb3fdd5633179eaf7ad76c267afcde","target":"graph","created_at":"2026-05-18T04:32:22Z","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 have introduced the notion of (1,2)-ideal in an LA-semigroup and shown that (1,2)-ideal and two-sided ideal coincide in an intra-regular LA-semigroup. We have characterized an intra-regular LA-semigroup by using the properties of left and right ideals. Some natural examples of LA-semigroups have been given. Further we have investigated some useful conditions for an LA-semigroup to become an intra-regular LA-semigroup and given the counter examples to illustrate the converse inclusions. All the ideals (left, right, two-sided, interior, quasi, bi- generalized bi- and (1,2)) of ","authors_text":"Faisal, Madad Khan, Venus Amjid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-27T11:41:34Z","title":"Ideals in intra-regular left almost semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5598","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:cd6dc28f28b625d3bc4a5318d68b6c8b04b2517f76d28bacc60ac986a223ea47","target":"record","created_at":"2026-05-18T04:32:22Z","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":"ebadf7119ce7f23af28e263a6b01277203b558424275bbed147626b806968594","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-12-27T11:41:34Z","title_canon_sha256":"d801f59b193995ac435d63fd92e0140e8c60a6e0e3969985ace92ebb74a5feec"},"schema_version":"1.0","source":{"id":"1012.5598","kind":"arxiv","version":1}},"canonical_sha256":"b02a12f0362bd10a349a2511883606c0bad04e4a271c857f0ea63179b7f0ecea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b02a12f0362bd10a349a2511883606c0bad04e4a271c857f0ea63179b7f0ecea","first_computed_at":"2026-05-18T04:32:22.864689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:22.864689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cyfpwr5GG5Q6tFn5HXhGIRqeCqoSWBfb5irTYZzWdkjuk3pQSkfM453aO+BWD876VBqQczQYvM65JrVtTagVBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:22.865492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd6dc28f28b625d3bc4a5318d68b6c8b04b2517f76d28bacc60ac986a223ea47","sha256:0ddda43de96af483fd26814fce723f30b9fb3fdd5633179eaf7ad76c267afcde"],"state_sha256":"86b69cdef619b46ebf91f33990d0ce15c892c65567b44bd6c5e9565c6afb0b87"}