On arithmetical associated orders
type: Item
instance of: scholarly article
title: On arithmetical associated orders
zbMATH Open document ID: 0857.11063
published in: Journal of Number Theory
publication date: 1996-08-05T00:00:00Z
review text: Let \(p\) be an odd prime, and \(L/K\) a totally ramified finite abelian extension of \(p\)-adic fields with Galois group \(G\). For each ideal \(I\) of the valuation ring of \(L\), the associated order \(\text{End}_{\mathbb{Q}_p [G]}(I)\) is an interesting invariant of the \(\mathbb{Z}_p [G]\)-structure of \(I\). The authors show that, unless \(G\) is cyclic, no such order can contain any idempotent of \(\mathbb{Q}_p [G]\) which does not already lie in \(\mathbb{Z}_p[G]\). This puts a strong restriction on the possible structures of these orders. An algorithm for computing associated orders is also described, and explicit examples are computed.
Mathematics Subject Classification ID: 11S23
Mathematics Subject Classification ID: 11Y40
zbMATH DE Number: 894612
zbMATH Keywords: totally ramified finite abelian extension of \(p\)-adic fields
zbMATH Keywords: associated order
zbMATH Keywords: algorithm
author: Werner Bley
author: David Burns
reviewed by: Thong Nguyen Quang Do
MaRDI profile type: Publication
full work available at URL: jnth.1996.0082
OpenAlex ID: W2050576750
DOI: 10.1006/JNTH.1996.0082
description: scientific article; zbMATH DE number 894612