nLab
Lazard's criterion

Context

Algebra

Homological algebra

homological algebra

and

nonabelian homological algebra

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Contents

Statement

Let RR be a commutative ring.

Proposition

(Lazard’s criterion)

An RR-module is a flat module precisely if it is a filtered colimit of free modules.

This is due to (Lazard (1964)). See at flat module for more.

References

  • Daniel Lazard, Sur les modules plats C. R. Acad. Sci. Paris 258, 6313–6316 (1964)
Created on October 17, 2012 22:40:38 by Urs Schreiber (82.169.65.155)