{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ZMU3LBIDC6JKZDHH3B2IFU4PNR","short_pith_number":"pith:ZMU3LBID","schema_version":"1.0","canonical_sha256":"cb29b585031792ac8ce7d87482d38f6c6bf8bb8056b0de39204e1f26416d7782","source":{"kind":"arxiv","id":"1010.2910","version":1},"attestation_state":"computed","paper":{"title":"Characterizations of Abel-Grassmann's groupoids by their intuitionistic fuzzy ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Faisal, Madad Khan","submitted_at":"2010-10-14T13:30:48Z","abstract_excerpt":"In this paper, we have introduced the concept of intuitionistic fuzzy ideals in an AG-groupoids. We have characterized regular and intra-regular AG-groupoids in terms of intuitionistic fuzzy left (right, two-sided) ideals, fuzzy (generalized) bi-ideals and intuitionistic fuzzy (1,2)-ideals. We have proved that all the intuitionistic fuzzy ideals coincides in regular and intra-regular AG-groupoids. It has been shown that the set of intuitionistic fuzzy two sided ideals of a regular AG-groupoid forms a semilattice structure. We have also given some useful conditions for an AG-groupoid to become "},"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":"1010.2910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-10-14T13:30:48Z","cross_cats_sorted":[],"title_canon_sha256":"f0a2146ba243b67e8e83af1149315487d9a7b3863b5b6b9bdd91614e74974f85","abstract_canon_sha256":"4963a2792ed4722f6d174f4c98065d2539b05c56676fd5f731fdd645240532be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:18.890657Z","signature_b64":"XNfK7Af6mrgiDUz9AMhv2x5jjBauyLczmroUgLwhGgfizmvRVMtU2D2BcOmRIwiya2JyelQO2VgVb3H4on0yAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb29b585031792ac8ce7d87482d38f6c6bf8bb8056b0de39204e1f26416d7782","last_reissued_at":"2026-05-18T04:39:18.889914Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:18.889914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations of Abel-Grassmann's groupoids by their intuitionistic fuzzy ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Faisal, Madad Khan","submitted_at":"2010-10-14T13:30:48Z","abstract_excerpt":"In this paper, we have introduced the concept of intuitionistic fuzzy ideals in an AG-groupoids. We have characterized regular and intra-regular AG-groupoids in terms of intuitionistic fuzzy left (right, two-sided) ideals, fuzzy (generalized) bi-ideals and intuitionistic fuzzy (1,2)-ideals. We have proved that all the intuitionistic fuzzy ideals coincides in regular and intra-regular AG-groupoids. It has been shown that the set of intuitionistic fuzzy two sided ideals of a regular AG-groupoid forms a semilattice structure. We have also given some useful conditions for an AG-groupoid to become "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2910","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":"1010.2910","created_at":"2026-05-18T04:39:18.890040+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.2910v1","created_at":"2026-05-18T04:39:18.890040+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2910","created_at":"2026-05-18T04:39:18.890040+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZMU3LBIDC6JK","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZMU3LBIDC6JKZDHH","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZMU3LBID","created_at":"2026-05-18T12:26:18.847500+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/ZMU3LBIDC6JKZDHH3B2IFU4PNR","json":"https://pith.science/pith/ZMU3LBIDC6JKZDHH3B2IFU4PNR.json","graph_json":"https://pith.science/api/pith-number/ZMU3LBIDC6JKZDHH3B2IFU4PNR/graph.json","events_json":"https://pith.science/api/pith-number/ZMU3LBIDC6JKZDHH3B2IFU4PNR/events.json","paper":"https://pith.science/paper/ZMU3LBID"},"agent_actions":{"view_html":"https://pith.science/pith/ZMU3LBIDC6JKZDHH3B2IFU4PNR","download_json":"https://pith.science/pith/ZMU3LBIDC6JKZDHH3B2IFU4PNR.json","view_paper":"https://pith.science/paper/ZMU3LBID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.2910&json=true","fetch_graph":"https://pith.science/api/pith-number/ZMU3LBIDC6JKZDHH3B2IFU4PNR/graph.json","fetch_events":"https://pith.science/api/pith-number/ZMU3LBIDC6JKZDHH3B2IFU4PNR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZMU3LBIDC6JKZDHH3B2IFU4PNR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZMU3LBIDC6JKZDHH3B2IFU4PNR/action/storage_attestation","attest_author":"https://pith.science/pith/ZMU3LBIDC6JKZDHH3B2IFU4PNR/action/author_attestation","sign_citation":"https://pith.science/pith/ZMU3LBIDC6JKZDHH3B2IFU4PNR/action/citation_signature","submit_replication":"https://pith.science/pith/ZMU3LBIDC6JKZDHH3B2IFU4PNR/action/replication_record"}},"created_at":"2026-05-18T04:39:18.890040+00:00","updated_at":"2026-05-18T04:39:18.890040+00:00"}