TORSION-FREE ABELIAN GROUPS WITH FINITE RANK ENDOMORPHISM RINGS

Abstract

We show that if A and C are torsion-free abelian groups with ∩{ker f|f: A → C} = 0 = ∩{ker g|g: C → A}, and if A has a left Artinian quasi-endomorphism ring then A and C share a nonzero quasi-summand. Some consequences explored.