Abstract

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.

Keywords

flat modules, projective covers

Mathematical Subject Classification

Primary: 16D40

Authors