On splitting the Knebusch-Milnor exact sequence
type: Item
instance of: scholarly article
title: On splitting the Knebusch-Milnor exact sequence
zbMATH Open document ID: 1158.11019
author: Przemysław Koprowski
published in: Journal of Algebra
publication date: 2006-12-07T00:00:00Z
review text: Let \(K\) be a formally real algebraic function field of one variable with real closed field of constants \(k\) and let \(\gamma(K)\) be the set of all points of \(K\), whose residue field is equal to \(k\). The set \(\gamma(K)\) may be viewed as a real algebraic curve. That curve is a disjoint union of finitely semi-algebraically connected components. The ring \(R\) of regular functions on \(\gamma(K)\) is a Dedekind domain, so its Witt ring \(WR\) can be embedded into the Witt ring \(WK\) of field \(K\). The main result of the paper states that the Witt ring \(WR\) is a direct summand of the group \(WK\). As a consequence of this theorem the Author shows that, in this case, the Knebusch-Milnor exact sequence slices into and is patched by two split exact sequences.
Mathematics Subject Classification ID: 11E81
Mathematics Subject Classification ID: 11E10
zbMATH DE Number: 5078124
zbMATH Keywords: Witt rings
zbMATH Keywords: Knebusch-Milnor exact sequence
zbMATH Keywords: real algebraic curves
reviewed by: Alfred Czogała
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.03.017
OpenAlex ID: W2009778814
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DOI: 10.1016/J.JALGEBRA.2006.03.017
description: scientific article; zbMATH DE number 5078124