Generalized Jordan left derivations on semiprime algebras

Let ${\mathcal{A}}$ be a semiprime algebra of characteristic not 2. Then any generalized Jordan left derivation on ${\mathcal{A}}$ is a generalized left derivation and is also a generalized derivation. This gives an affirmative answer to a question in Ashraf and Ali (Bull Korean Math Soc 45:253–261, 2008). Moreover, we prove that there are no nonzero generalized Jordan left derivations that take only nilpotent values on ${\mathcal{A}}$ .     

Generalized Jordan left derivations on semiprime algebras

Let A{\mathcal{A}} be a semiprime algebra of characteristic not 2. Then any generalized Jordan left derivation on A{\mathcal{A}} is a generalized left derivation and is also a generalized derivation. This gives an affirmative answer to a question in Ashraf and Ali (Bull Korean Math Soc 45:253–261, 2008). Moreover, we prove that there are no nonzero generalized Jordan left derivations that take only nilpotent values on A{\mathcal{A}} .     

Generalized Jordan derivations on Lie ideals associate with Hochschild 2-cocycles of rings

Let R be a 2-torsion free ring and L be a Lie ideal of R. In this paper we initiate the study of generalized derivations on Lie ideals associate with Hochschild 2-cocycles and prove that every generalized derivation associate with a Hochschild 2-cocycle on L is a generalized derivation on L under certain conditions.     

Generalized Jordan derivations associated with Hochschild 2-cocycles of triangular algebras

In this paper, we investigate a new type of generalized derivations associated with Hochschild 2-cocycles which is introduced by A.Nakajima (Turk. J. Math. 30 (2006), 403–411). We show that if U is a triangular algebra, then every generalized Jordan derivation of above type from U into itself is a generalized derivation.     

A note on Jordan derivations of triangular rings

Aequationes mathematicae - In this note we prove that every Jordan derivation on a triangular ring is a derivation. Moreover, we show that, under some conditions, every Jordan derivation on a...     

Generalized Jordan derivations on triangular matrix algebras

In this note, we prove that every generalized Jordan derivation from the algebra of all upper triangular matrices over a commutative ring with identity into its bimodule is the sum of a generalized derivation and an antiderivation.     

三角代数上的广义Jordan导子

主要研究了三角代数上的广义Jordan导子．利用三角代数上广义Jordan导子和广义内导子的联系．证明了作用在一个含单位元的可交换环上的三角代数到其自身上的环线性广义Jordan导子是一个广义导子．     

Generalized left derivations acting as homomorphisms and anti-homomorphisms on Lie ideal of rings

Let R be a prime ring with characteristic different from 2 and L be a Lie ideal of R. In this paper, we characterize generalized left derivation, which acts as a homomorphisms or an anti-homomorphisms on L.