{"paper":{"title":"Characterizations of Jordan mappings on some rings and algebras through zero products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jiankui Li, Jun He, Wenbo Huang","submitted_at":"2016-11-14T07:44:38Z","abstract_excerpt":"Let $\\mathcal{U}=\\left[\n  \\begin{array}{cc}\n  \\mathcal{A} & \\mathcal{M}\n  \\mathcal{N}& \\mathcal{B}\n  \\end{array}\n  \\right]$ be a generalized matrix ring, where $\\mathcal{A}$ and $\\mathcal{B}$ are 2-torsion free. We prove that if $\\phi :\\mathcal{U}\\rightarrow \\mathcal{U}$ is an additive mapping such that $\\phi(U)\\circ V+U\\circ \\phi(V)=0$ whenever $UV=VU=0,$ then $\\phi=\\delta+\\eta$, where $\\delta$ is a Jordan derivation and $\\eta$ is a multiplier. As its applications, we prove that the similar conclusion remains valid on full matrix algebras, unital prime rings with a nontrivial idempotent, unit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04274","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"}