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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 ∈ ℕ of 𝔄 is automatically an additive higher derivation on 𝔄 . Moreover, 𝒟 = { δ n } n ∈ ℕ is an inner * -higher derivation.

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