Lattice Modules over Principal Element Domains

Abstract

This paper obtains a structure theorem for a finitely generated lattice module 𝔐 over a Noetherian principal element domain 𝔏,with a slightly stronger theorem if the lattice module satisfies a hypothesis valid over principal ideal domains. Additionally,we obtain a new characterization of Dedekind lattice domains as multiplicative lattice domains over which there exists a non torsion,principally generated,Noetherian join-principal-element lattice module.