Decomposability of ideals in splitting \(p\)-extensions of local fields
type: Item
instance of: scholarly article
title: Decomposability of ideals in splitting \(p\)-extensions of local fields
zbMATH Open document ID: 0841.11059
published in: Vestnik St. Petersburg University. Mathematics
publication date: 1996-02-07T00:00:00Z
review text: Let \(k\) be a \(p\)-adic number field. A finite extension \(K\) of \(k\) is called splitting if it is the composite of an unramified and a fully ramified subextension. Let \(K/k\) be a normal extension and let \(O\) be the ring of integral elements in \(k\). An ideal of \(K\) is called decomposable if it is decomposable as \(O[G(K/ k)]\)-module. The main result of the author is the following theorem: Let \(K/k\) be a normal splitting \(p\)-extension and let \(p\neq 2\). Then \(K\) contains decomposable ideals if and only if the ramification index of \(K/k\) divides the different of \(K/k\).
Mathematics Subject Classification ID: 11S15
zbMATH DE Number: 815591
zbMATH Keywords: \(p\)-adic number field
zbMATH Keywords: splitting \(p\)-extension
zbMATH Keywords: decomposable ideals
author: S. V. Vostokov
reviewed by: Helmut Koch
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 815591