Generalized Higher Derivations on ΓM-Modules

The concepts of generalized higher derivations, Jordan generalized higher derivations, and Jordan generalized triple higher derivations on Γ-ring M into ΓM-modules X are presented. We prove that every Jordan generalized higher derivation of Γ-ring M into 2-torsion free ΓM-module X, such that aαbβc=aβbαc, for all a, b, c M and α,βΓ, is Jordan generalized triple higher derivation of M into X.

n-Commuting skew higher derivation on semiprime rings

In this article we study skew higher derivation (d_i)_{i\in \mathbb{N}} on semiprime ring R with suitable torsion restriction and we prove that every n-centralizing skew higher derivation is n-commuting. Further, we show that if a ring R has n-centralizing skew higher derivation then either R is commutative or some linear combination of (d_i)_{i\in \mathbb{N}} maps center of R to zero.

Generalized Jordan triple (σ,τ)-higher derivation on triangular algebras

Let R be a commutative ring with unity, U = Tri(A,M,B) be a triangular algebra consisting of unital algebras A,B and (A,B)-bimodule M which is faithful as a left A-module and also as a right B-module. Let ? and ? be two automorphisms of U. A family ? = {?n}n?N of R-linear mappings ?n : U ? U is said to be a generalized Jordan triple (?,?)-higher derivation on A if there exists a Jordan triple (?,?)-higher derivation D = {dn}n?N on U such that ?0 = IU, the identity map of U and ?n(XYX) = ?i+j+k=n ?i(?n-i(X))dj(?k?i(Y))dk(?n-k(X)) holds for all X,Y ? U and each n ? N. In this article, we study generalized Jordan triple (?,?)-higher derivation on A and prove that every generalized Jordan triple (?,?)-higher derivation on U is a generalized (?,?)-higher derivation on U.

On Jordan triple (σ,τ)-higher derivation of triangular algebra

Let R be a commutative ring with unity, A = Tri(A,M,B) be a triangular algebra consisting of unital algebras A,B and (A,B)-bimodule M which is faithful as a left A-module and also as a right B-module. In this article,we study Jordan triple (σ,τ)-higher derivation onAand prove that every Jordan triple (σ,τ)-higher derivation on A is a (σ,τ)-higher derivation on A.

Nonlinear *-Lie Higher Derivations of Standard Operator Algebras

Let ℌ be an in finite-dimensional complex Hilbert space and A be a standard operator algebra on ℌ which is closed under the adjoint operation. It is shown that every nonlinear *-Lie higher derivation D = {δn}gn∈N of A is automatically an additive higher derivation on A. Moreover, D = {δn}gn∈N is an inner *-higher derivation.

Approximation of additive functional equations in NA Lie C*-algebras

In this paper, by using fixed point method, we approximate a stable map of higher *-derivation in NA C*-algebras and of Lie higher *-derivations in NA Lie C*-algebras associated with the following additive functional equation,where m ≥ 2.

Notes on the higher derivations on prime rings

The main purpose of thess notes investigated some certain properties and relation between higher derivation (HD,for short) and Lie ideal of semiprime rings and prime rings,we gave some results about that.

Generalized Higher Derivations on Lie Ideals of Triangular Algebras

Let be the triangular algebra consisting of unital algebras A and B over a commutative ring R with identity 1 and M be a unital (A; B)-bimodule. An additive subgroup L of A is said to be a Lie ideal of A if [L;A] ⊆ L. A non-central square closed Lie ideal L of A is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on A, every generalized Jordan triple higher derivation of L into A is a generalized higher derivation of L into A.