{"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"}