GENERALIZED HIGHER DERIVATIONS

Local higher derivations on C*-algebras are higher derivations

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

Generalized (σ , τ) higher derivations in prime rings

Let R be a ring and U be a Lie ideal of R. Suppose that σ, τ are endomorphisms of R. A family D = {d n } n ∈ N of additive mappings d n :R → R is said to be a (σ,τ)- higher derivation of U into R if d 0 = I R , the identity map on R and [Formula: see text] holds for all a, b ∈ U and for each n ∈ N. A family F = {f n } n ∈ N of additive mappings f n :R → R is said to be a generalized (σ,τ)- high...

Generalized higher (U,M)-derivations in prime Γ-Rings

Let M be a 2-torsion free prime Γ-ring satisfying the condition a α b β c=a β b α c,∀a,b,c∈M and α,β∈Γ, U be an admissible Lie ideal of M and F=(f i ) i∈N be a generalized higher (U,M)-derivation of M with an associated higher (U,M)-derivation D=(d i ) i∈N of M. Then for all n∈N we prove that [Formula: see text]. Mathematics Subject Classification (2010): 13N15; 16W10; 17C50.

Generalized Jordan Triple Higher ∗−Derivations on Semiprime Rings

Let R be an associative ring not necessarily with identity element. For any x, y ∈ R. Recall that R is prime if xRy = 0 implies x = 0 or y = 0, and is semiprime if xRx = 0 implies x = 0. Given an integer n ≥ 2, R is said to be n−torsion free if for x ∈ R, nx = 0 implies x = 0.An additive mapping d : R → R is called a derivation if d(xy) = d(x)y + yd(x) holds for all x, y ∈ R, and it is called a...

Prime Higher Derivations on Algebras