Singular elements and the Witt equivalence of rings of algebraic integers
type: Item
instance of: scholarly article
title: Singular elements and the Witt equivalence of rings of algebraic integers
zbMATH Open document ID: 1175.11019
author: Beata Rothkegel
author: Alfred Czogała
published in: The Ramanujan Journal
publication date: 2009-06-16T00:00:00Z
review text: Singular elements of a ring of \(S\)-integers of a global field are meant to be the non-zero elements of the field having even \(\mathfrak{p}\)-orders at all primes \(\mathfrak{p}\) not in \(S\). The authors study the group of singular elements in quadratic extensions of global fields, and in the case when the class number of the ring of \(S\)-integers is odd, they find a basis for the group (modulo squares). This is then used to discuss the existence of isomorphisms between the Witt rings of \(S\)- and \(S'\)-integers in two global fields \(K\) and \(K'\). The most complete results are obtained in the case of biquadratic extensions of nonreal number fields and of global function fields. In these cases necessary and sufficient conditions are found for the existence of strong isomorphisms between Witt rings of \(S\)- and \(S'\)-integers.
reviewed by: Kazimierz Szymiczek
Mathematics Subject Classification ID: 11E12
Mathematics Subject Classification ID: 11E81
zbMATH DE Number: 5565210
zbMATH Keywords: Hasse domain
zbMATH Keywords: global field
zbMATH Keywords: singular element
zbMATH Keywords: bicyclic number field
zbMATH Keywords: Witt ring
zbMATH Keywords: isomorphism of Witt rings
MaRDI profile type: Publication
full work available at URL: s11139-008-9119-z
OpenAlex ID: W2060466182
cites work: Q3994474
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DOI: 10.1007/S11139-008-9119-Z
description: scientific article; zbMATH DE number 5565210