Spectrally bounded generalized inner derivations

Generalized Derivations on Modules

String Vertices and Inner Derivations

We show that it is algebraically consistent to express the string field theory operators ∂, K and I as inner derivations of the B-V algebra of string vertices. In this approach, the recursion relations for the string vertices are found to take the form of a ‘geometrical’ quantum master equation, 1 2{B,B} + ∆B = 0. We also show that the B-V delta operator cannot be an inner derivation on the alg...

Derivations and bounded nilpotence index

We construct a nil ring R which has bounded index of nilpotence 2, is Wedderburn radical, and is commutative, and which also has a derivation δ for which the differential polynomial ring R[x; δ] is not even prime radical. This example gives a strong barrier to lifting certain radical properties from rings to differential polynomial rings. It also demarcates the strength of recent results about ...

Generalized Derivations on Modules *

Let A be a Banach algebra and M be a Banach left A-module. A linear map δ : M → M is called a generalized derivation if there exists a derivation d : A → A such that δ(ax) = aδ(x) + d(a)x (a ∈ A,x ∈ M). In this paper, we associate a triangular Banach algebra T to Banach A-module M and investigate the relation between generalized derivations on M and derivations on T . In particular, we prove th...

Nearly Generalized Jordan Derivations

Let A be an algebra and let X be an A-bimodule. A C−linear mapping d : A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ : A → X such that d(a) = ad(a) + δ(a)a for all a ∈ A. The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.