Generalized Derivations on Prime Rings with Involution

Adel Alahmadi, Husain Alhazmi, Shakir Ali, Abdul Nadim Khan

Abstract


Let \(R\) be an associative ring. An additive mapping \(F : R \to R\) is called a generalized derivation with an associated derivation \(d\) of \(R\) if it satisfies \(F(xy) = F(x)y + xd(y)\) for all \(x, y \in R\). In the present paper, we obtain description of the structure of \(R\) and information about the generalized derivation \(F\) which satisfies certain \(\ast\)-differential identities on prime rings with involution.

Keywords


Generalized derivation; Derivation; Involution and prime ring

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References


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