Trace forms of dyadic number fields
type: Item
instance of: scholarly article
title: Trace forms of dyadic number fields
zbMATH Open document ID: 0731.11021
DOI: 10.1016/0022-314X(91)90024-6
author: Martin Epkenhans
published in: Journal of Number Theory
publication date: 1991-01-01T00:00:00Z
review text: The trace form associated with a finite separable field extension K/k is the quadratic map \(x\to trace_{K/k} x^ 2\) defined on the k-vector space K. The appearance of trace forms in Witt classes of quadratic forms over algebraic number fields and local fields was studied by \textit{P. E. Conner} and \textit{R. Perlis} [A survey of trace forms of algebraic number fields (World Sci. 1984; Zbl 0551.10017)]. In this paper their results are complemented by an explicit characterization in terms of invariants of quadratic forms of those quadratic forms over the field \({\mathbb{Q}}_ 2\) of dyadic numbers which are isometric to trace forms of finite extensions \(K/{\mathbb{Q}}_ 2.\) \{P. E. Conner's name is misspelled throughout the paper.\}
Mathematics Subject Classification ID: 11E08
Mathematics Subject Classification ID: 12F10
zbMATH DE Number: 4208159
zbMATH Keywords: trace form
zbMATH Keywords: finite separable field extension
zbMATH Keywords: quadratic map
zbMATH Keywords: dyadic numbers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4208159