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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"},"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":"1611.04274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-14T07:44:38Z","cross_cats_sorted":[],"title_canon_sha256":"8502754294627af38305d725d90e9e00900a75deb29927ed53b77a0b4b5f42a7","abstract_canon_sha256":"e078a1421bc76a8b86d5965737de452cefd0bcb05a49ecbd4f93f2afcc942b7d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:16.982945Z","signature_b64":"uXwnO3FGbz5mfwpBQrxzK5nZcm2HR7JQeB07+MgYEQ1CGDvmKmmyftmVi/YoblQUtpwR0pd/6/YRsOWeDF54DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9f8826f221bc45510323b7d6b98cc94851aca5abae02707a672960eb3969db0","last_reissued_at":"2026-05-18T00:59:16.982275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:16.982275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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