Every Cotorsion-Free Ring is an Endomorphism Ring

Abstract

Some years ago A. L. S. Corner proved that every countable and cotorsion-free ring can be realized as the endomorphism ring of some torsion-free abelian group. This result has many interesting consequences for abelian groups. Using a set-theoretic axiom ∇k., which follows for instance from V = L, we can drop the countability condition in Corner's theorem.