Countable ℵ 0-indecomposable mixed abelian groups of finite torsion-free rank

Abstract

A group is called Et,-indecomposable if it does not have a decomposition into a direct sum of N, non-zero summands. This work is devoted to the study of K,-indecomposable countable mixed abelian groups of finite torsion-free rank in the most general setting. Theorem 1’ proven here has main results of [6, Theorem 23 and [4, Theorem 33 as corollaries: let T be a countable reduced torsion abelian group, and R a torsion-free abelian group of finite rank n. There exists an Et,-indecomposable abelian group G with the torsion part T and G/T% R if and only if a basic subgroup B of T can be decomposed into a direct sum B = @ ;= O Bi such that 1 B, 1 < K,,