Flat modules and lifting of finitely generated projective modules

We introduce nets in rings, which turn out to describe right flat modules and left flat modules over a fixed ring R at the same time. As an application we prove that for a finitely generated projective right R/J(R)-module P, there exists a finitely generated flat right R-module M with M/MJ(R) isomorphic to P if and only if there exists a projective left R-module P′ with P′/J(R) P′ isomorphic to the dual of P.