Editing Flat module (section)

=== Torsion-free modules ===

Every flat module is [[torsion-free module|torsion-free]].<!-- with the appropriate definition of torsion-free, the ring need not be a domain.--> This results from the above characterization in terms of relations by taking {{math|1=''m'' = 1}}.

The converse holds over the integers, and more generally over [[principal ideal domain]]s and [[Dedekind ring]]s.

An integral domain over which every torsion-free module is flat is called a [[Prüfer domain]].