Philippine E-Journals

On Some Results of a Torsion-Free Abelian Kernel Group

Ricky B. Villeta

Discipline: Mathematics

 

Abstract:

In [6], for any torsion-free abelian groups G and H , the kernel of H in G is ()() G H f fHom H G ker , kerÎ , =I . The kernel of H in G is a pure fully invariant subgroup of G. A torsion-free abelian group G is a kernel group if M =ker(G,G M ) for every pure fully invariant subgroup M of G. This paper shall give further results and characterizations of the direct sum of a kernel and kernel groups of a torsion-free abelian group.