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On Jordan Left Derivations

On Jordan Left Derivations
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Jordan, Jordan Right and Jordan Left Derivations on Convolution Algebras

Bulletin of the Iranian Mathematical Society, 2018
A Jordan derivation on a ring $R$ is an additive mapping $d$ that satisfies \[ d(x^2) = d(x) x + x d(x) \] for all $x \in R$; $d$ is said to be a Jordan left derivation if \[ d(x^2) = 2xd(x) \] for all $x \in R$. Jordan right derivations are defined similarly.
Ahmadi Gandomani, Mohammad Hossein, Mehdipour, Mohammad Javad   +1 more
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Additivity of Jordan Derivations on Jordan Algebras with Idempotents

Bulletin of the Iranian Mathematical Society, 2022
Additivity is one of the most active topics in the study of mappings on rings and operator algebras. The aim of this paper is to study the additivity of Jordan derivations on Jordan algebras. The following result is obtained. Let \(J\) be a Jordan algebra with a nontrivial idempotent \(e\) and let \(J=J_1\oplus J_{\frac{1}{2}}\oplus J_0\) be the Peirce
Ferreira, Bruno L. M., Fošner, Ajda, Moraes, Gabriela C.   +2 more
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JORDAN *-DERIVATIONS OF PRIME RINGS

Journal of Algebra and Its Applications, 2014
Let R be a prime ring, which is not commutative, with involution * and with Qms(R) the maximal symmetric ring of quotients of R. An additive map δ : R → R is called a Jordan *-derivation if δ(x2) = δ(x)x* + xδ(x) for all x ∈ R. A Jordan *-derivation of R is called X-inner if it is of the form x ↦ xa - ax* for x ∈ R, where a ∈ Qms(R).
Lee, Tsiu-Kwen, Zhou, Yiqiang
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Derivations on Banach-Jordan Pairs

The Quarterly Journal of Mathematics, 2001
A classical topic in the theory of Banach structures is the automatical continuity of derivations. From 1968, when Johnson and Sinclair proved the continuity of derivations acting on semisimple associative Banach algebras, until now, several algebraic conditions on a Banach algebra \(A\) which ensure the continuity of its derivations have been ...
Fernández López, A., Marhnine, H., Zarhouti, C.   +2 more
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Jordan Higher Derivations of Incidence Algebras

Bulletin of the Malaysian Mathematical Sciences Society, 2021
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Lizhen Chen, Zhankui Xiao
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Nonlinear *-Jordan-type derivations on *-algebras

Rocky Mountain Journal of Mathematics, 2021
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Li, Changjing, Zhao, Yuanyuan, Zhao, Fangfang   +2 more
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Mixed *-Jordan-type derivations on *-algebras

Journal of Algebra and Its Applications, 2022
Let [Formula: see text] be an *-algebra with identity [Formula: see text] and [Formula: see text] and [Formula: see text] nontrivial symmetric idempotents in [Formula: see text]. In this paper we study the characterization of nonlinear mixed *-Jordan-type derivations.
Ferreira, Bruno Leonardo Macedo, Wei, Feng   +1 more
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