Regular ideals in commutative rings, sublattices of regular ideals, and Prüfer rings

D. D Anderson; J Pascual

doi:10.1016/0021-8693(87)90226-2

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Regular ideals in commutative rings, sublattices of regular ideals, and Prüfer rings

Journal article

Open access

Peer reviewed

Regular ideals in commutative rings, sublattices of regular ideals, and Prüfer rings

D. D Anderson and J Pascual

Journal of Algebra, Vol.111(2), pp.404-426

1987

DOI: 10.1016/0021-8693(87)90226-2

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Abstract

In this paper we investigate regularly generated, regular, 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.

Details

Title: Subtitle: Regular ideals in commutative rings, sublattices of regular ideals, and Prüfer rings
Creators: D. D Anderson
J Pascual
Resource Type: Journal article
Publication Details: Journal of Algebra, Vol.111(2), pp.404-426
DOI: 10.1016/0021-8693(87)90226-2
ISSN: 0021-8693
eISSN: 1090-266X
Language: English
Date published: 1987
Academic Unit: Mathematics
Record Identifier: 9983985853702771

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