On a division ring with discrete valuation
type: Item
instance of: scholarly article
title: On a division ring with discrete valuation
zbMATH Open document ID: 0826.16014
author: Kozo Sugano
published in: Hokkaido Mathematical Journal
publication date: 1995-06-13T00:00:00Z
review text: A division ring \(A\) with non-trivial valuation \(\nu\) has the completion \(A^*\) with respect to the \(\nu\)-topology, which is also a division ring. If \(B\) is a division subring of \(A\), then the closure \(B^*\) of \(B\) in \(A^*\), with respect to the \(\nu\)-topology, is isomorphic to the completion of \(B\) as a topological ring. The purpose of the author's paper is to show that \(B^*\) coincides with the double centralizer of \(B\) in \(A^*\) for each division \(C\)-subalgebra \(B\) of \(A\) (where \(C\) is the center of \(A\)), when \(A\) is finite over \(C\) and \(\nu\) is discrete.
Mathematics Subject Classification ID: 16K20
Mathematics Subject Classification ID: 16W80
Mathematics Subject Classification ID: 16W60
zbMATH DE Number: 720796
zbMATH Keywords: division ring
zbMATH Keywords: valuation
zbMATH Keywords: completion
zbMATH Keywords: \(\nu\)-topology
zbMATH Keywords: topological ring
zbMATH Keywords: double centralizer
zbMATH Keywords: center
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381413096
OpenAlex ID: W2099027180
DOI: 10.14492/HOKMJ/1381413096
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description: scientific article; zbMATH DE number 720796