Torsion-free E-modules (Q1100238)

A module M over a unital commutative ring R is called an E-module if every additive homomorphism from R into M is a module homomorphism. While this definition seems very specialized, E-modules play an important role in the study of torsion-free abelian groups. In this paper the authors characterize finite rank E-modules M over finite rank torsion-free rings R. They first reduce the problem to the case in which R is an integrally closed subring of an algebraic number field F and M is semi-local, and then characterize M in terms of the Galois structure of F over \({\mathbb{Q}}\).