Integral domains that lose ideals in overrings
type: Item
instance of: scholarly article
title: Integral domains that lose ideals in overrings
zbMATH Open document ID: 0651.13002
published in: Pacific Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: We study domains with the property that, in any proper overring, some proper ideal extends to the unit ideal, and domains with the property that, in any proper overring, some proper ideal of a certain type (v- ideal, invertible ideal, or principal ideal) extends to the unit ideal. We characterize the Noetherian domains with these properties, and we show that even the strongest of these properties does not imply the QR- property.
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 4061365
zbMATH Keywords: extension to unit ideal
zbMATH Keywords: Kronecker function ring
zbMATH Keywords: v-ideal
zbMATH Keywords: invertible ideal
zbMATH Keywords: principal ideal
zbMATH Keywords: Noetherian domains
zbMATH Keywords: QR-property
author: William J. Heinzer
author: David C. Lantz
MaRDI profile type: Publication
full work available at URL: pjm.1990.145.223
OpenAlex ID: W1986457215
DOI: 10.2140/PJM.1990.145.223
description: scientific article; zbMATH DE number 4061365