Flat modules and lifting of finitely generated projective modules

Alberto Facchini, Dolors Herbera and Iskhak Sakhajev

Vol. 220 (2005), No. 1, 49–68

DOI: 10.2140/pjm.2005.220.49

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 2000

Primary: 16D40

Milestones

Received: 11 July 2003

Revised: 13 July 2004

Accepted: 10 August 2004

Published: 1 May 2005