Abelian groups whose nonzero endomorphisms have nonessential kernels

作者：Alizade Rafail^*; Isah Surajo Ibrahim

来源：Journal of Algebra and Its Applications, 2017, 16(3): 1750048.

DOI：10.1142/S0219498817500487

• K-singular subgroup
• K-nonsingular abelian group
• pure subgroup
• basic subgroup

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.

• 出版日期2017-3