Maximal orders having a discrete normalizing class group
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.
scientific article; zbMATH DE number 3952983