Anneaux de Dedekind dont le groupe des classes est fini (Q799742)

A module over a ring A is said to be n-acc if every increasing chain of submodules generated by n elements is stationary. An integral domain A is said to satisfy \(P_ n\) if every torsion-free n-acc A-module of rank n is finitely generated. The main result is a: Dedekind domain satisfies \(P_ n\) if and only if its ideal class group is finite.