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Commutative Rings Whose Finitely Generated Ideals are Quasi-Flat

In: Rings, Polynomials, and Modules

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  • François Couchot

    (Normandie Université)

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.

Suggested Citation

  • François Couchot, 2017. "Commutative Rings Whose Finitely Generated Ideals are Quasi-Flat," Springer Books, in: Marco Fontana & Sophie Frisch & Sarah Glaz & Francesca Tartarone & Paolo Zanardo (ed.), Rings, Polynomials, and Modules, pages 129-143, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-65874-2_7
    DOI: 10.1007/978-3-319-65874-2_7
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