Generalized identities with invertible variables for subrings of artinian rings

Let $R$ be a prime subring with 1 of the matrix ring $D_k$ over a skew field $D$, $k\geq1$. Suppose that the center $C$ of $R$ is infinite and elements of $C$ belong to the center of $D_k$. Let $G$ be an elementary absolute irreducible subgroup of the group $U(R)$ of invertible elements of $R$ with a nonzero generalized identity with invertible variables $f\in R\langle X,X^{-1}\rangle$, then $R$ is a $PI$-ring.