Torsionless Modules and Minimal Generating Sets for Ideals of Integral Domains

Abstract

This is a treatise of relationships between the number of elements necessary to generate the ideals of a domain and the torsionless modules of that domain. Three types of domains are identified according to natural decompositions of their torsionless modules. The descriptions of the domains follow the historical approach of Dedekind by focusing on the ideals of the domains.