{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2TUMOV2NPTQVPSNIQXHGBBEJIE","short_pith_number":"pith:2TUMOV2N","schema_version":"1.0","canonical_sha256":"d4e8c7574d7ce157c9a885ce608489411af12b82de51eddbbc2501533718508a","source":{"kind":"arxiv","id":"1202.2527","version":1},"attestation_state":"computed","paper":{"title":"Jordan Derivations and Antiderivations of Generalized Matrix Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Feng Wei, Leon van Wyk, Yanbo Li","submitted_at":"2012-02-12T13:30:37Z","abstract_excerpt":"Let $\\mathcal{G}=[A & M   N & B]$ be a generalized matrix algebra defined by the Morita context $(A, B,_AM_B,_BN_A, \\Phi_{MN}, \\Psi_{NM})$. In this article we mainly study the question of whether there exist proper Jordan derivations for the generalized matrix algebra $\\mathcal{G}$. It is shown that if one of the bilinear pairings $\\Phi_{MN}$ and $\\Psi_{NM}$ is nondegenerate, then every antiderivation of $\\mathcal{G}$ is zero. Furthermore, if the bilinear pairings $\\Phi_{MN}$ and $\\Psi_{NM}$ are both zero, then every Jordan derivation of $\\mathcal{G}$ is the sum of a derivation and an antideri"},"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":"1202.2527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-12T13:30:37Z","cross_cats_sorted":[],"title_canon_sha256":"1ce6de5811b47f374eaf9fdfbcff646616d7c19590e396a196e6f9875d001704","abstract_canon_sha256":"0c01331a3e834e4572f0299ff25f77e61493f9aacbc96f8a17dfdacbc0bd519c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:26.279271Z","signature_b64":"OqjlJniYW315rFqbhjL98zPGSoXs7AO+xh+Onz6YfoCukBuTPxikp1J5GCEtZpNVaP3YBGh1A0fRVWgNTnRFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4e8c7574d7ce157c9a885ce608489411af12b82de51eddbbc2501533718508a","last_reissued_at":"2026-05-18T04:02:26.278679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:26.278679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Jordan Derivations and Antiderivations of Generalized Matrix Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Feng Wei, Leon van Wyk, Yanbo Li","submitted_at":"2012-02-12T13:30:37Z","abstract_excerpt":"Let $\\mathcal{G}=[A & M   N & B]$ be a generalized matrix algebra defined by the Morita context $(A, B,_AM_B,_BN_A, \\Phi_{MN}, \\Psi_{NM})$. In this article we mainly study the question of whether there exist proper Jordan derivations for the generalized matrix algebra $\\mathcal{G}$. It is shown that if one of the bilinear pairings $\\Phi_{MN}$ and $\\Psi_{NM}$ is nondegenerate, then every antiderivation of $\\mathcal{G}$ is zero. Furthermore, if the bilinear pairings $\\Phi_{MN}$ and $\\Psi_{NM}$ are both zero, then every Jordan derivation of $\\mathcal{G}$ is the sum of a derivation and an antideri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2527","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":"1202.2527","created_at":"2026-05-18T04:02:26.278758+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.2527v1","created_at":"2026-05-18T04:02:26.278758+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2527","created_at":"2026-05-18T04:02:26.278758+00:00"},{"alias_kind":"pith_short_12","alias_value":"2TUMOV2NPTQV","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2TUMOV2NPTQVPSNI","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2TUMOV2N","created_at":"2026-05-18T12:26:50.516681+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/2TUMOV2NPTQVPSNIQXHGBBEJIE","json":"https://pith.science/pith/2TUMOV2NPTQVPSNIQXHGBBEJIE.json","graph_json":"https://pith.science/api/pith-number/2TUMOV2NPTQVPSNIQXHGBBEJIE/graph.json","events_json":"https://pith.science/api/pith-number/2TUMOV2NPTQVPSNIQXHGBBEJIE/events.json","paper":"https://pith.science/paper/2TUMOV2N"},"agent_actions":{"view_html":"https://pith.science/pith/2TUMOV2NPTQVPSNIQXHGBBEJIE","download_json":"https://pith.science/pith/2TUMOV2NPTQVPSNIQXHGBBEJIE.json","view_paper":"https://pith.science/paper/2TUMOV2N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.2527&json=true","fetch_graph":"https://pith.science/api/pith-number/2TUMOV2NPTQVPSNIQXHGBBEJIE/graph.json","fetch_events":"https://pith.science/api/pith-number/2TUMOV2NPTQVPSNIQXHGBBEJIE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2TUMOV2NPTQVPSNIQXHGBBEJIE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2TUMOV2NPTQVPSNIQXHGBBEJIE/action/storage_attestation","attest_author":"https://pith.science/pith/2TUMOV2NPTQVPSNIQXHGBBEJIE/action/author_attestation","sign_citation":"https://pith.science/pith/2TUMOV2NPTQVPSNIQXHGBBEJIE/action/citation_signature","submit_replication":"https://pith.science/pith/2TUMOV2NPTQVPSNIQXHGBBEJIE/action/replication_record"}},"created_at":"2026-05-18T04:02:26.278758+00:00","updated_at":"2026-05-18T04:02:26.278758+00:00"}