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$(σ, τ)$ -derivations on prime near rings

Mohammad Ashraf; Asma Ali; Shakir Ali — 2004

Archivum Mathematicum

There is an increasing body of evidence that prime near-rings with derivations have ring like behavior, indeed, there are several results (see for example [1], [2], [3], [4], [5] and [8]) asserting that the existence of a suitably-constrained derivation on a prime near-ring forces the near-ring to be a ring. It is our purpose to explore further this ring like behaviour. In this paper we generalize some of the results due to Bell and Mason [4] on near-rings admitting a special type of derivation...

Nonlinear $*$ -Lie higher derivations of standard operator algebras

Mohammad Ashraf; Shakir Ali; Bilal Ahmad Wani — 2018

Communications in Mathematics

Let $ℋ$ be an infinite-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 $𝒟 = {δ_{n}}_{n \in ℕ}$ of $𝔄$ is automatically an additive higher derivation on $𝔄$ . Moreover, $𝒟 = {δ_{n}}_{n \in ℕ}$ is an inner $*$ -higher derivation.