Geodesic
Net rings normalized by a nonsplit maximal torus
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 113-119 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate net rings $M(\sigma)$ normalized by a torus $T=T(d)$, which is the image of the multiplicative group of the radical extension $K=k(\sqrt[n]d)$ (of degree $n$ of a field $k$, $char(k)\neq2$) under the regular embedding into $G=GL(n,k)$. It is shown that the structure of these net rings is determined by a certain subring of the ground field $k$. Necessary and sufficient conditions are obtained for the normalizability of a net ring $M(\sigma)$ by the torus $T=T(d)$ for the case when the ground field $k=\mathbb Q$ is the field of rational numbers. We also study transvection modules and factor rings of intermediate subgroups $H$, $T\subseteq H\subseteq G$.
Mots-clés : net, nonsplit maximal torus
Keywords: net ring, intermediate subgroup. 
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N. A. Dzhusoeva. Net rings normalized by a nonsplit maximal torus. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 113-119. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a10/

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