Lie Triple Derivable Mappings on Rings

Let ℛ be a ring containing a nontrivial idempotent. In this article, under a mild condition on ℛ, we prove that if δ is a Lie triple derivable mapping from ℛ into ℛ, then there exists a Z A, B (depending on A and B) in its centre (ℛ) such that δ(A + B) = δ(A) + δ(B) + Z A, B . In particular, let ℛ b...

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Bibliographic Details
Published in:Communications in algebra 2014-06, Vol.42 (6), p.2510-2527
Main Authors: Li, Changjing, Fang, Xiaochun, Lu, Fangyan, Wang, Ting
Format: Article
Language:English
Subjects:
Additives
Additivity
Algebra
Centroids
Closures
Derivation
Lie triple derivable mappings
Mapping
Nest algebras
Prime rings
Triangular algebras
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Summary:Let ℛ be a ring containing a nontrivial idempotent. In this article, under a mild condition on ℛ, we prove that if δ is a Lie triple derivable mapping from ℛ into ℛ, then there exists a Z A, B (depending on A and B) in its centre (ℛ) such that δ(A + B) = δ(A) + δ(B) + Z A, B . In particular, let ℛ be a prime ring of characteristic not 2 containing a nontrivial idempotent. It is shown that, under some mild conditions on ℛ, if δ is a Lie triple derivable mapping from ℛ into ℛ, then δ = D + τ, where D is an additive derivation from ℛ into its central closure T and τ is a mapping from ℛ into its extended centroid such that τ(A + B) = τ(A) + τ(B) + Z A, B and τ([[A, B], C]) = 0 for all A, B, C ∈ ℛ.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2012.763041