{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WDZHG7FK6Y4WB6RKTVOUT4UBID","short_pith_number":"pith:WDZHG7FK","schema_version":"1.0","canonical_sha256":"b0f2737caaf63960fa2a9d5d49f28140c63c2c024bc42e5f824d9dad44687310","source":{"kind":"arxiv","id":"1007.0791","version":2},"attestation_state":"computed","paper":{"title":"On subgroups in division rings of type $2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bui Xuan Hai, Mai Hoang Bien, Trinh Thanh Deo","submitted_at":"2010-07-06T01:34:35Z","abstract_excerpt":"Let $D$ be a division ring with center $F$. We say that $D$ is a {\\em division ring of type $2$} if for every two elements $x, y\\in D,$ the division subring $F(x, y)$ is a finite dimensional vector space over $F$. In this paper we investigate multiplicative subgroups in such a ring."},"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":"1007.0791","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-07-06T01:34:35Z","cross_cats_sorted":[],"title_canon_sha256":"184689d00c9cccab791598ba4608a8547927dc4dcba6e9558900c609111497e9","abstract_canon_sha256":"800827c75e737fddbd88c526a2752cdcd885bcf0c36f24b7e64c36428e9f56f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:07.069303Z","signature_b64":"T7KwPsU45p6dflh20SI61/ReXnk/FK4okul2I9SdDHaKdeexgSwxupscAwirb8EDixT4YgRTgIzSGoug04QkDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0f2737caaf63960fa2a9d5d49f28140c63c2c024bc42e5f824d9dad44687310","last_reissued_at":"2026-05-17T23:53:07.068762Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:07.068762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On subgroups in division rings of type $2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bui Xuan Hai, Mai Hoang Bien, Trinh Thanh Deo","submitted_at":"2010-07-06T01:34:35Z","abstract_excerpt":"Let $D$ be a division ring with center $F$. We say that $D$ is a {\\em division ring of type $2$} if for every two elements $x, y\\in D,$ the division subring $F(x, y)$ is a finite dimensional vector space over $F$. In this paper we investigate multiplicative subgroups in such a ring."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0791","kind":"arxiv","version":2},"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":"1007.0791","created_at":"2026-05-17T23:53:07.068854+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.0791v2","created_at":"2026-05-17T23:53:07.068854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0791","created_at":"2026-05-17T23:53:07.068854+00:00"},{"alias_kind":"pith_short_12","alias_value":"WDZHG7FK6Y4W","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"WDZHG7FK6Y4WB6RK","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"WDZHG7FK","created_at":"2026-05-18T12:26:15.391820+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/WDZHG7FK6Y4WB6RKTVOUT4UBID","json":"https://pith.science/pith/WDZHG7FK6Y4WB6RKTVOUT4UBID.json","graph_json":"https://pith.science/api/pith-number/WDZHG7FK6Y4WB6RKTVOUT4UBID/graph.json","events_json":"https://pith.science/api/pith-number/WDZHG7FK6Y4WB6RKTVOUT4UBID/events.json","paper":"https://pith.science/paper/WDZHG7FK"},"agent_actions":{"view_html":"https://pith.science/pith/WDZHG7FK6Y4WB6RKTVOUT4UBID","download_json":"https://pith.science/pith/WDZHG7FK6Y4WB6RKTVOUT4UBID.json","view_paper":"https://pith.science/paper/WDZHG7FK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.0791&json=true","fetch_graph":"https://pith.science/api/pith-number/WDZHG7FK6Y4WB6RKTVOUT4UBID/graph.json","fetch_events":"https://pith.science/api/pith-number/WDZHG7FK6Y4WB6RKTVOUT4UBID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WDZHG7FK6Y4WB6RKTVOUT4UBID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WDZHG7FK6Y4WB6RKTVOUT4UBID/action/storage_attestation","attest_author":"https://pith.science/pith/WDZHG7FK6Y4WB6RKTVOUT4UBID/action/author_attestation","sign_citation":"https://pith.science/pith/WDZHG7FK6Y4WB6RKTVOUT4UBID/action/citation_signature","submit_replication":"https://pith.science/pith/WDZHG7FK6Y4WB6RKTVOUT4UBID/action/replication_record"}},"created_at":"2026-05-17T23:53:07.068854+00:00","updated_at":"2026-05-17T23:53:07.068854+00:00"}