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We obtain the (necessary and) sufficient conditions for a Lie n-derivation {\\phi} on A to be of the form {\\phi}=d+{\\delta}+{\\gamma}, where d is a derivation on A, {\\delta} is a singular Jordan derivation on A and {\\gamma} is a linear mapping from A into the centre Z(A) vanishing on all (n-1)-th commutators of A. In particular, we also discuss the (necessary and) sufficient conditions for a Lie n-derivation {\\"},"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":"1702.08877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-02-27T10:45:43Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"078a07df8a82a80edc3c745da9ea9be994bbab232f7f1514f1a876dc4be2362e","abstract_canon_sha256":"6ccc79eb9776cae65741778265a8d458227c680ffd1c4a93852c5246bb3d65c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:47.684202Z","signature_b64":"gjSPnIMCD62UESCQArpfCnWdas8UTuVd7ucAoTpPJv4tpRPS4mHogbhQOgd535MvRLpMbp91S2TgqcM93brCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"692827c1492119960d02314101f52202d7fd21b6bbd6b30910c812bd9fa6d878","last_reissued_at":"2026-05-18T00:49:47.683583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:47.683583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations of Lie n-derivations of unital algebras with nontrivial idempotents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"Jiankui Li, Yana Ding","submitted_at":"2017-02-27T10:45:43Z","abstract_excerpt":"Let A be a unital algebra with a nontrivial idempotent e, and f=1-e. Suppose that A satisfies that exe.eAf={0}=fAe.exe implies exe=0 and eAf.fxf={0}=fxf.fAe implies fxf=0 for each x in A. We obtain the (necessary and) sufficient conditions for a Lie n-derivation {\\phi} on A to be of the form {\\phi}=d+{\\delta}+{\\gamma}, where d is a derivation on A, {\\delta} is a singular Jordan derivation on A and {\\gamma} is a linear mapping from A into the centre Z(A) vanishing on all (n-1)-th commutators of A. 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