Duality in Noetherian integral domains
type: Item
instance of: scholarly article
title: Duality in Noetherian integral domains
zbMATH Open document ID: 0940.13016
author: H. Pat Goeters
published in: Rocky Mountain Journal of Mathematics
publication date: 2000-02-03T00:00:00Z
full work available at URL: CONT29-2.html
review text: Let \(A\) be a torsion-free abelian group of rank one and let \(C(A)\) denote the class of torsion-free abelian groups \(M\) of finite rank such that \(M\) embeds as \(\text{End}(A)\)-submodule of \(A^n\) for some \(n\). Then the map \(M\) to \(\Hom(M,A)\) on \(C(A)\) defines a duality. This is called Warfield duality. In this paper, the author gives a direct and simpler proof that a Noetherian domain is Warfield exactly when each ideal is two-generated.
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 1356455
zbMATH Keywords: Warfield duality
zbMATH Keywords: Noetherian domain
zbMATH Keywords: two-generated ideal
reviewed by: Kwangil Koh
MaRDI profile type: Publication
OpenAlex ID: W1998622758
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DOI: 10.1216/RMJM/1181071650
description: scientific article; zbMATH DE number 1356455