Nonlinear Jordan derivations of incidence algebras

Yang, Yichuan

doi:10.1080/00927872.2021.1890106

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2022

2023

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Cited by 4 publications

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“…Ten the question, what maps on a ring R are automatically additive was considered and diferent results were obtained in this line, we refer the reader to [2,3] and references therein for more details. Especially, it has been proved on special rings that every derivable map or Jordan derivable map is additive, for instance, see [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Characterizing Jordan Derivable Maps on Triangular Rings by Local Actions

Ghahramani

Ghosseiri

Rezaei

2022

Journal of Mathematics

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Suppose that T = Tri A , ℳ , ℬ is a 2-torsion free triangular ring, and S = A , B | A B = 0 , A , B ∈ T ∪ A , X | A ∈ T , X ∈ P , Q , where P is the standard idempotent of T and Q = I − P . Let δ : T ⟶ T be a mapping (not necessarily additive) satisfying, A , B ∈ S ⇒ δ A ∘ B = A ∘ δ B + δ A ∘ B , where A ∘ B = A B + B A is the Jordan product of T . We obtain various equivalent conditions for δ , specifically, we show that δ is an additive derivation. Our result generalizes various results in these directions for triangular rings. As an application, δ on nest algebras are determined.

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