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Fundamentalnaya i Prikladnaya Matematika, 1995, Volume 1, Issue 3, Pages 661–668
(Mi fpm94)
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This article is cited in 2 scientific papers (total in 2 papers)
On the general linear group over weak Noetherian associative algebras
I. Z. Golubchik Bashkir State Pedagogical University
Abstract:
Let $R$ be a weak Noetherian algebra with unity element over an infinite field, $I$ an ideal in $R$, $n\geq3$, $E_n(R)$ the elementary subgroup in the general linear group $GL_n(R)$, $E_n(R,I)$ the normal subgroup in $E_n(R)$ generated by the elementary matrices $1+\lambda e_{ij}$, $\lambda\in I$, $1\leq i\neq j\leq n$, $GL_n(R,I)$ the kernel and $C_n(R,I)$ the preimage of the center of the homomorphism $GL_n(R)\to GL_n(R/I)$ respectively. It is proved that if $G$ is a subgroup of $GL_n(R)$, then it is normalized by $E_n(R)$ if and only if $E_n(R,F)\subseteq G\subseteq C_n(R,F)$ for some ideal $F$ of $R$; $[C_n(R,F),E_n(R)]=E_n(R,F)$ and in particular the groups $E_n(R)$ and $E_n(R,F)$ are normal in $GL_n(R)$ for all ideals $F$ of $R$.
Received: 01.04.1995
Citation:
I. Z. Golubchik, “On the general linear group over weak Noetherian associative algebras”, Fundam. Prikl. Mat., 1:3 (1995), 661–668
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https://www.mathnet.ru/eng/fpm94 https://www.mathnet.ru/eng/fpm/v1/i3/p661
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Abstract page: | 262 | Full-text PDF : | 107 | References: | 47 | First page: | 2 |
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