  The aim of this paper is to describe the classes of strongly flat and weakly
cotorsion modules with respect to a multiplicative subset or a finite
collection of multiplicative subsets in a commutative ring. The strongly flat
modules are characterized by a set of conditions, while the weakly cotorsion
modules are produced by a generation procedure. Passing to the collection of
all countable multiplicative subsets, we define quite flat and almost cotorsion
modules, and show that, over a Noetherian ring with countable spectrum, all
flat modules are quite flat and all almost cotorsion modules are cotorsion.
