Duality in Noetherian integral domains
Let \(A\) be a torsion-free abelian group of rank one and let \(C(A)\) denote the class of torsion-free abelian groups \(M\) of finite rank such that \(M\) embeds as \(\text{End}(A)\)-submodule of \(A^n\) for some \(n\). Then the map \(M\) to \(\Hom(M,A)\) on \(C(A)\) defines a duality. This is called Warfield duality. In this paper, the author gives a direct and simpler proof that a Noetherian domain is Warfield exactly when each ideal is two-generated.
scientific article; zbMATH DE number 1356455
scientific article