Decomposition of ideals in abelian \(p\)-extensions of complete discrete valuation fields
type: Item
instance of: scholarly article
title: Decomposition of ideals in abelian \(p\)-extensions of complete discrete valuation fields
zbMATH Open document ID: 0949.11059
DOI: 10.1007/BF02169959
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-10-05T00:00:00Z
review text: Decomposition of ideals as Galois modules is studied here. Let \(k\) be a local field of characteristic zero, complete with a discrete valuation, having a residue field of characteristic \(p > 2\). Let \(K/k\) be a totally ramified cyclic extension of degree \(p^m\). The authors find a decomposition for any ideal \(A\) of \(K\) as an \(O[G]\)-module, where \(O\) is the ring of integers of \(k,G=\text{Gal}(K/k)\). Earlier, they gave conditions for an ideal \(A\) being decomposable as \(O[G]\)-module in [Decomposability of ideals as Galois modules in complete discrete valuation fields, St. Petersbg. Math J. 11, No. 2, 233-249 (2000); translation from Algebra Anal. 11, No. 2, 41-63 (1999; Zbl 0964.11054)]. The more general case where \(K/k\) is an abelian \(p\)-extension could be deduced to the above case.
reviewed by: Xianke Zhang
Mathematics Subject Classification ID: 11S15
Mathematics Subject Classification ID: 11R33
zbMATH DE Number: 1337563
zbMATH Keywords: decomposition of ideals
zbMATH Keywords: Galois modules
zbMATH Keywords: local field
zbMATH Keywords: discrete valuation
zbMATH Keywords: cyclic extension
author: Mikhail V. Bondarko
author: S. V. Vostokov
MaRDI profile type: Publication
cites work: Q4396663
cites work: Q4940667
cites work: Q4094965
cites work: Q3136423
description: scientific article; zbMATH DE number 1337563