Commutative Rings Whose Finitely Generated Ideals are Quasi-Flat

François Couchot ()
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François Couchot: Normandie Université

A chapter in Rings, Polynomials, and Modules, 2017, pp 129-143 from Springer

Abstract: Abstract A definition of quasi-flat left module is proposed and it is shown that any left module which is either quasi-projective or flat is quasi-flat. A characterization of local commutative rings for which each ideal is quasi-flat (resp. quasi-projective) is given. It is also proven that each commutative ring R whose finitely generated ideals are quasi-flat is of λ-dimension ≤ 3, and this dimension ≤ 2 if R is local. This extends a former result about the class of arithmetical rings. Moreover, if R has a unique minimal prime ideal, then its finitely generated ideals are quasi-projective if they are quasi-flat.

Keywords: Quasi-flat module; Chain ring; Arithmetical ring; fqf-ring; fqp-ring; λ-Dimension; 13F05; 13B05; 13C13; 16D40; 16B50; 16D90 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-65874-2_7

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DOI: 10.1007/978-3-319-65874-2_7

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