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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 thatfor any Krull domain  R  withwheredenotes the class of all strong  w -modules anddenotes the class of-torsionfree  R -modules  N  with the property thatfor all  w -projective  R -modules  M  and all integers

On w ∞ -projective modules and Krull domains