Commutative rings whose finitely generated ideals are quasi-flat

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.