On relative integral bases for pure quartic fields
type: Item
instance of: scholarly article
title: On relative integral bases for pure quartic fields
zbMATH Open document ID: 0762.11038
author: John A. Hymo
author: Charles J. Parry
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1992-10-13T00:00:00Z
review text: Let \(K=\mathbb{Q}[z]\), \(z^ 4\in\mathbb{Q}\), be a pure quartic field with Galois closure \(L\). For any quadratic extension \(L/L_ 1\), the authors determine whether \(L/L_ 1\) has an integral basis, and similarly for any quadratic extension \(K/K_ 1\). The results are based on a criterion of \textit{H. B. Mann} [Proc. Am. Math. Soc. 9, 167-172 (1958; Zbl 0081.266)]: \(E/F\), quadratic, has an integral basis iff the discriminant ideal \(\Delta_{E/F}\) is principal, \(\Delta_{E/F}=(D)\) for some \(D\) in \(F\) such that \(E=F(\sqrt D)\).
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R04
zbMATH DE Number: 68887
zbMATH Keywords: pure quartic field
zbMATH Keywords: Galois closure
zbMATH Keywords: integral basis
zbMATH Keywords: quadratic extension
reviewed by: Lindsay N. Childs
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 68887