Coseparable torsionfree Abelian groups
The author develops a concept of coseparability, dual to separability, for torsion-free abelian groups of arbitrary nonmeasurable rank and establishes several important properties. A group G is coseparable if every pure subgroup of finite corank contains a summand of G which has a completely decomposable finite rank complement. Vector groups are coseparable, but not vice versa. Finite rank coseparable groups are completely decomposable, but countable rank ones need not be. Coseparability is closed under products and summands, but not sums.
completely decomposable finite rank complement
scientific article; zbMATH DE number 3906752