Regular ideals in commutative rings, sublattices of regular ideals, and Prüfer rings
type: Item
instance of: scholarly article
title: Regular ideals in commutative rings, sublattices of regular ideals, and Prüfer rings
zbMATH Open document ID: 0641.13003
DOI: 10.1016/0021-8693(87)90226-2
author: B. George
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: We quote from the authors' introduction: ``In this paper we investigate regularly generated, semiregular, and faithful ideals in a commutative ring R and the sublattices they determine. Connections with multiplicative lattice theory are given. Given a Prüfer ring R we show that there is a Prüfer domain D with the sublattice of regular ideals of R isomorphic to the lattice of ideals of D. Numerous examples of rings with zero divisors having certain properties are given. A Prüfer ring with an invertible ideal that is not generated by regular elements is constructed. An example is given to show that the intersection of two regular principal ideals need not be generated by regular elements.'' The potential reader should note that the mentioned properties are equivalent for ideals in a noetherian ring.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 4043967
zbMATH Keywords: ideals
zbMATH Keywords: sublattices
zbMATH Keywords: Prüfer ring
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90226-2
OpenAlex ID: W2027745368
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description: scientific article; zbMATH DE number 4043967