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ON SKEW JORDAN PRODUCT AND GENERALIZED DERIVATIONS IN PRIME RINGS WITH INVOLUTION
Keywords:
involution, skew Jordan product, generalized derivation, prime ringDOI:
https://doi.org/10.17654/0972555524020Abstract
Let $\mathcal{S}$ be a ring with involution. Then the skew Jordan product of two elements $u$ and $v$ in $\mathcal{S}$ is defined by $u \diamond v=u v+v u^*$. A map $\mathcal{F}: \mathcal{S} \rightarrow \mathcal{S}$ is considered to be a generalized derivation if it is additive and has a derivation $\delta$ such that $\mathcal{F}(u v)=\mathcal{F}(u) v+u \delta(v)$ for all $u, v \in \mathcal{S}$. The purpose of this paper is to characterize certain functional identities related to the skew Jordan product with prime rings.
Received: January 22, 2024
Revised: March 8, 2024
Accepted: April 26, 2024
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