On w(infinity)-projective modules and Krull domains

Let R be a commutative ring with identity. In this paper, w(infinity)-projective modules are introduced and studied. It is shown that every R-module has a special w(infinity)-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(infinity)-projective R-module is w(infinity)-projective. And we show that P-w(dagger infinity) subset of(not equal) W-infinity for any Krull domain R with pd(R)Q = 2, where W-infinity denotes the class of all strong w-modules and P-w(dagger infinity) denotes the class of GV-torsionfree R-modules N with the property that Ext(R)(k)(M, N) = 0 for all w-projective R-modules M and all integers k >= 1.