Abstract: We studied the w-module theoretic analogue of P-flat modules by using w-module theory over commutative rings. Firstly, we introduced the concept of w-P-flat modules over commutative rings and discussed several characterizations and properties of w-P-flat modules. Secondly, as applications of w-P-lat modules, we give some new characterizations of von Neumann regular rings and p.p rings (i.e., rings in which every principle ideal is a projective ideal).

Key words: w-P-flat module, p.p ring, w-p.f ring