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Fundam. Prikl. Mat., 1995, Volume 1, Issue 4, Pages 1101–1105 (Mi fpm112)  

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.

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Bibliographic databases:
UDC: 512.544.6+512.552.4
Received: 01.04.1995

Citation: I. Z. Golubchik, “Generalized identities with invertible variables for subrings of artinian rings”, Fundam. Prikl. Mat., 1:4 (1995), 1101–1105

Citation in format AMSBIB
\Bibitem{Gol95}
\by I.~Z.~Golubchik
\paper Generalized identities with invertible variables for subrings of artinian rings
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 4
\pages 1101--1105
\mathnet{http://mi.mathnet.ru/fpm112}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1791794}
\zmath{https://zbmath.org/?q=an:0868.16020}


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  • Фундаментальная и прикладная математика
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