On w∞ -projective modules and Krull domains

Abstract

Let R be a commutative ring with identity. In this paper, w∞ -projective modules are introduced and studied. It is shown that every R-module has a special w∞ -projective precover. As an application, it is proved that a domain R is a Krull domain if and only if every submodule of a w∞ -projective R-module is w∞ -projective. And we show that for any Krull domain R with where denotes the class of all strong w-modules and denotes the class of -torsionfree R-modules N with the property that for all w-projective R-modules M and all integers