Integer valued functions with countable support (Q1065155)

For an arbitrary index set \(I\) let \(Z^{[I]}\) be the subgroup of \(Z^ I\) consisting of all elements \(a\), whose support \(\text{supp}(a)=\{i\in I\mid a(i)\neq 0\}\) is countable. The author proves that for any set \(I\), every epimorphic image of the group \(Z^{[J]}\) is isomorphic to a direct sum of a group \(Z^{[I]}\), where \(| J| \leq | I|\), and a cotorsion group.