Flatness, LCM-stability, and related module-theoretic properties

D. D Anderson; David E Dobbs

doi:10.1016/0021-8693(88)90138-X

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Flatness, LCM-stability, and related module-theoretic properties

Journal article

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Flatness, LCM-stability, and related module-theoretic properties

D. D Anderson and David E Dobbs

Journal of algebra, Vol.112(1), pp.139-150

1988

DOI: 10.1016/0021-8693(88)90138-X

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Abstract

The relationship between flatness and LCM-stability is clarified by the following two results. A finitely generated ideal I of an integral domain is flat if and only if I is n -flat for some integer n ⩾ 2. There exists an integral domain with a nonflat ideal J = ( a , b , c ) such that Jab ∩ Jac ∩ Jbc = J ( ab , ac , bc ). Next, related module-theoretic properties, (∗∗) and (∗), respectively weaker than projectivity and flatness, are introduced. Under appropriate finiteness conditions, these properties are preserved by certain inverse limits. Their study leads to new characterizations of quasicomplete local rings and coherent integral domains.

Details

Title: Subtitle: Flatness, LCM-stability, and related module-theoretic properties
Creators: D. D Anderson
David E Dobbs
Resource Type: Journal article
Publication Details: Journal of algebra, Vol.112(1), pp.139-150
DOI: 10.1016/0021-8693(88)90138-X
ISSN: 0021-8693
eISSN: 1090-266X
Language: English
Date published: 1988
Academic Unit: Mathematics
Record Identifier: 9983985869402771

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