Journal of the
Korean Mathematical Society JKMS

Let $\mathcal{R}$ be a prime ring of characteristic different from 2, $\mathcal{Q}_r$ be its right Martindale quotient ring and $\mathcal{C}$ be its extended centroid. Suppose that $\mathcal{G}$ is a nonzero generalized skew derivation of $\mathcal{R}$, $\alpha$ is the associated automorphism of $\mathcal{G}$, $f(x_1, \ldots, x_n)$ is a non-central multilinear polynomial over $\mathcal{C}$ with $n$ non-commuting variables and $\mathcal{S}=\{f(r_1,\ldots,r_n) \,|\, r_1,\ldots,r_n \in \mathcal{R}\}$. If $\mathcal{G}$ acts as a Jordan homomorphism on $\mathcal{S}$, then either $\mathcal{G}(x)=x$ for all $x\in \mathcal{R}$, or $\mathcal{G}=\alpha$.

Keywords: polynomial identity, generalized skew derivation, prime ring

MSC numbers: 16W25, 16N60