Commutative rings in which every ideal is a product of primary ideals

D. D Anderson; L. A Mahaney

doi:10.1016/0021-8693(87)90014-7

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Commutative rings in which every ideal is a product of primary ideals

Journal article

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Commutative rings in which every ideal is a product of primary ideals

D. D Anderson and L. A Mahaney

Journal of algebra, Vol.106(2), pp.528-535

1987

DOI: 10.1016/0021-8693(87)90014-7

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Abstract

A Q -ring is a commutative ring in which every ideal is a product of primary ideals. We show that R is a Q -ring if and only if R is a Laskerian ring (every ideal has a primary decomposition) and every nonmaximal prime ideal of R is finitely generated and locally principal. We also show that R [ X ] or R [ X ] is a Q -ring if and only if R is a finite direct product of Dedekind domains and special principal ideal rings.

Details

Title: Subtitle: Commutative rings in which every ideal is a product of primary ideals
Creators: D. D Anderson
L. A Mahaney
Resource Type: Journal article
Publication Details: Journal of algebra, Vol.106(2), pp.528-535
DOI: 10.1016/0021-8693(87)90014-7
ISSN: 0021-8693
eISSN: 1090-266X
Language: English
Date published: 1987
Academic Unit: Mathematics
Record Identifier: 9983985864302771

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