A new lower bound for corresponding residue systems in normal, totally ramified extensions of number fields
type: Item
instance of: scholarly article
title: A new lower bound for corresponding residue systems in normal, totally ramified extensions of number fields
zbMATH Open document ID: 0860.11068
author: Steven R. Benson
published in: Illinois Journal of Mathematics
publication date: 1997-04-08T00:00:00Z
review text: Let \(F\) be a finite extension of \(\mathbb{Q}_p\). Assume that \(K\), \(K'\) and \(L\) are finite extensions of \(F\) such that \(L\), \(K\), \(K'\) are normal over \(F\), \(KK' \subset L\) and \(K\), \(K'\) are linearly disjoint over \(F\). The author gives a lower bound for the largest integer \(m = M_L(K,K')\) satisfying \[ {\mathfrak O}_K + {\mathfrak P}^m = {\mathfrak O}_{K'} + {\mathfrak P}^m \] in the case when \(L/F\) is totally ramified, where \({\mathfrak P}\) is the (unique) maximal ideal of \({\mathfrak O}_L\). A global version of the result is also presented.
Mathematics Subject Classification ID: 11S15
Mathematics Subject Classification ID: 11R04
zbMATH DE Number: 878724
zbMATH Keywords: residue systems
zbMATH Keywords: totally ramified extensions
zbMATH Keywords: \(p\)-adic fields
zbMATH Keywords: lower bound
reviewed by: Witold Więsław
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 878724