Some facts concerning integral representations of the ideals in an algebraic number field
type: Item
instance of: scholarly article
title: Some facts concerning integral representations of the ideals in an algebraic number field
zbMATH Open document ID: 0434.12004
DOI: 10.1016/0024-3795(80)90223-2
published in: Linear Algebra and its Applications
publication date: 1980-01-01T00:00:00Z
review text: This paper studies the application of ideal matrices [the author, Arch. Math. 13, 275--282 (1962; Zbl 0118.27504)] in a regular representation of the maximal order of an algebraic number field \(F\). By a theorem of \textit{C. C. MacDuffee} [Math. Ann. 105, 663--665 (1931; Zbl 0003.10005)] the ideal matrix of an ideal is the right (or left) gcd of the maps of the elements in the ideal. This matrix is determined up to a unimodular matrix factor. If it lies inside the map of the ideal then we have a principal ideal. If it does not lie inside for any unimodular factor (on the appropriate side) then it does not commute with all the maps of the ideal. Further discussions of the ideal matrix are included.
Mathematics Subject Classification ID: 11R33
zbMATH DE Number: 3676012
zbMATH Keywords: integral representations of ideals
zbMATH Keywords: algebraic integers
zbMATH Keywords: ideal matrix
author: O. Taussky Todd
MaRDI profile type: Publication
full work available at URL: 0024-3795(80)90223-2
OpenAlex ID: W4205355835
cites work: Q4754499
cites work: Ideal matrices. I
cites work: A method for determining the canonical basis of an ideal in an algebraic field
description: scientific article; zbMATH DE number 3676012