nLab Lazard's criterion

Contents

Context

Algebra

Homological algebra

homological algebra

(also nonabelian homological algebra)

Introduction

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Schanuel's lemma

Homology theories

Theorems

Contents

Statement

Let RR be a commutative ring. (or maybe any 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)

Last revised on November 3, 2015 at 11:39:18. See the history of this page for a list of all contributions to it.