Norms and generalized class groups
type: Item
instance of: scholarly article
title: Norms and generalized class groups
zbMATH Open document ID: 0655.13003
DOI: 10.1016/0022-4049(88)90005-9
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let R be a commutative domain and s an idempotent kernel functor on the category of R-modules. An R-module is s-closed if it is isomorphic to its s-localization. Let (R,s)-mod denote the category of s-closed R-modules and R-homomorphisms. There is a ``tensor product'' in (R,s)-mod obtained by taking the s-localization of the ordinary tensor product. The author defines notions of s-separable and s-étale using the s-tensor product and then defines a norm functor for s-étale extensions. It has the expected properties, and induces the appropriate maps on s-Picard and s- Brauer groups. Since the class group of a Krull domain is an s-Picard group and the reflexive Brauer group is an s-Brauer group, this gives a norm map on those groups also.
Mathematics Subject Classification ID: 14F22
Mathematics Subject Classification ID: 13D99
zbMATH DE Number: 4069029
zbMATH Keywords: idempotent kernel functor
zbMATH Keywords: s-tensor product
zbMATH Keywords: s-Brauer groups
zbMATH Keywords: s-Picard group
author: Alain Verschoren
reviewed by: Andy R. Magid
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90005-9
OpenAlex ID: W2034959345
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description: scientific article; zbMATH DE number 4069029