Maximal orders having a discrete normalizing class group
type: Item
instance of: scholarly article
title: Maximal orders having a discrete normalizing class group
zbMATH Open document ID: 0593.16004
DOI: 10.1016/0021-8693(86)90086-4
author: Lieven Le Bruyn
author: Alain Verschoren
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let \(\Lambda\) be a maximal order (over a normal noetherian domain R) in a central simple algebra \(\Sigma\) over its field of fractions K; and let NC\(\ell (\Lambda)\) be the normalizing class group of \(\Lambda\). The first result proved by the authors is a generalization of a result of V. I. Danilov; viz. that the natural morphism NC\(\ell (\Lambda)\to NC\ell (\Lambda [t])\) splits. They say that \(\Lambda\) has a discrete normalizing class group if the above morphism is an isomorphism. They prove that \(\Lambda\) has a discrete class group when R has a discrete class group. Finally, they prove that, when \(\Lambda\) is Azumaya over R, and \(\Lambda\) has a discrete normalizing class group then R has a discrete class group.
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 14F22
zbMATH DE Number: 3952983
zbMATH Keywords: Azumaya algebra
zbMATH Keywords: maximal order
zbMATH Keywords: central simple algebra
zbMATH Keywords: normalizing class group
zbMATH Keywords: discrete normalizing class group
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90086-4
OpenAlex ID: W1967151274
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description: scientific article; zbMATH DE number 3952983