Commutative rings in which every ideal is a product of primary ideals
type: Item
instance of: scholarly article
title: Commutative rings in which every ideal is a product of primary ideals
zbMATH Open document ID: 0607.13004
DOI: 10.1016/0021-8693(87)90014-7
author: L. A. Mahaney
author: D. D. Anderson
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: The authors characterize the commutative rings with identity in which every ideal is a finite product of primary ideals. They call a ring with this property a Q-ring. They show that R is a Q-ring if and only if R is Laskerian (every ideal in R has a primary decomposition) and every nonmaximal prime ideal of R is finitely generated and locally principal. They prove that the polynomial ring R[X] or the formal power series ring \(RX\) is a Q-ring if and only if R is a general ZPI-ring, that is, R is a finite direct product of Dedekind domains and special principal ideal rings.
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13F25
Mathematics Subject Classification ID: 13C05
zbMATH DE Number: 3981304
zbMATH Keywords: finite product of primary ideals
zbMATH Keywords: Q-ring
zbMATH Keywords: Laskerian
zbMATH Keywords: polynomial ring
zbMATH Keywords: formal power series ring
zbMATH Keywords: Dedekind domains
zbMATH Keywords: principal ideal rings
reviewed by: William J. Heinzer
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90014-7
OpenAlex ID: W2044769080
cites work: Noetherian Rings in Which Every Ideal is a Product of Primary Ideals
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cites work: The Laskerian property in commutative rings
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cites work: Rings with Noetherian spectrum
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description: scientific article; zbMATH DE number 3981304