Indecomposability of ideals of \(\mathfrak p\)-adic number fields
type: Item
instance of: scholarly article
title: Indecomposability of ideals of \(\mathfrak p\)-adic number fields
zbMATH Open document ID: 1047.11112
author: Yoshimasa Miyata
published in: Journal of Number Theory
publication date: 2004-08-06T00:00:00Z
review text: Let \(p\) be an odd prime and let \(K/k\) be a \(p\)-extension of local fields with Galois group \(G\). The author proves that any ideal \(A\) of \(K\) is \(O[G]\)-indecomposable if and only if \(| G_1|\) does not divide the different \(D_{K/k}\). Here \(O\) denotes the ring of integers of \(k\) and \(G_1\) denotes the first ramification group of \(K/k\). \textit{S. V. Vostokov} [Vestn. St. Petersbg. Univ., Math. 26, No. 2, 10--21 (1993; Zbl 0841.11059)] proved the same result in the special case that \(K\) is the composite of an unramified extension with a fully ramified extension of \(k\).
Mathematics Subject Classification ID: 11S15
Mathematics Subject Classification ID: 11S20
zbMATH DE Number: 2083526
zbMATH Keywords: Galois module structure
zbMATH Keywords: Local fields
zbMATH Keywords: Ideals
zbMATH Keywords: Indecomposability
reviewed by: Helmut Koch
MaRDI profile type: Publication
full work available at URL: j.jnt.2004.03.001
OpenAlex ID: W2002973714
cites work: Q3922829
cites work: Q4722208
cites work: Q3992534
cites work: Vertices of ideals of a \({\mathfrak p}\)-adic number field
cites work: Decomposability of ideals in splitting \(p\)-extensions of local fields
DOI: 10.1016/J.JNT.2004.03.001
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description: scientific article; zbMATH DE number 2083526