Let R be a commutative ring, M be an R-module, and w be the so-called w-operation on R. Set S w={f∈ R [X]| c (f) w= R}, where c (f) denotes the content of f. Let R {X}= R [X] S w and M {X}= M [X] S w be the w-Nagata ring of R and the w-Nagata module of M respectively. Then we introduce and study two concepts of w-projective modules and w-invertible modules, which both generalize projective modules. To do so, we use two main methods of which one is to localize at maximal w-ideals of R and the other is to utilize w-Nagata modules over w-Nagata rings. In particular, it is shown that an R-module M is w-projective of finite type if and only if M {X} is finitely generated projective over R {X}; M is w-invertible if and only if M {X} is invertible over R {X}. As applications, it is shown that R is semisimple if and only if every R-module is w-projective and that, in a Q 0-PVMR, every finite type semi-regular module is w-projective.