Short communications

Generalized identities with invertible variables for subrings of artinian rings

I. Z. Golubchik

Bashkir State Pedagogical University

Abstract: 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.

UDC: 512.544.6+512.552.4

Received: 01.04.1995

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