Abelian groups whose nonzero endomorphisms have nonessential kernels

Abstract

In this paper we describe completely the K-singular subgroup of an abelian group and a K-nonsingular abelian group in terms of the basic subgroups of its p-components and the quotient group by the torsion part. We also prove that a pure subgroup and a quotient group by a pure subgroup of a K- nonsingular abelian group are K-nonsingular and give a condition under which a pure extension of a K-nonsingular abelian group by a K-nonsingular group is K-nonsingular.