Strongly Flat Modules over Matlis Domains

Strongly flat modules were introduced by Bazzoni–Salce 3 Bazzoni , S. , Salce , L. ( 2003 ). Almost perfect domains . Colloq. Math. 95 : 285 – 301 .Crossref] , Google Scholar]] and used to characterize almost perfect domains. Here we wish to study strongly flat modules, more generally, over Matlis domains; these are integral domains R such that the field of quotients Q has projective dimension 1. In Section 2, criteria are proved for strong flatness. We also prove that over arbitrary domains, strongly flat submodules of projective modules are projective (Theorem 3.2), in particular, strongly flat ideals are projective (Corollary 3.4) and use these results to show that the strongly flat dimension (which makes sense over Matlis domains) coincides with the projective dimension whenever it is > 1.