Lattice modules over principal element domains

摘要

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-clement lattice module. References: 12