Stacked Bases for Countable Homogeneous Completely Decomposable Groups

Abstract

Let A X be two homogeneous completely decomposable torsion free abelian groups of the same type t and of countable rank such that the quotient X =A is a direct sum of torsion cyclic groups and a homogeneous completely decomposable summand of type t. Furthermore assume that A and X have a common direct summand of countable rank. We show that there exist stacked bases for A and X , i.e. there existThis proves a stacked bases theorem for pairs of homogeneous completely decomposable torsion free abelian groups of countable rank and the same type with a large common summand.