Splitting kernels into small summands. (Q1760331)

Let \(\lambda\) be a regular cardinal. An epimorphism of Abelian groups is \(\lambda\)-pure if it is projective with respect to Abelian groups of size less than \(\lambda\). The authors show that cotorsion groups \(A\) with torsion \(tA\) are \(\lambda\)-pure projective for \(\lambda>|A/tA|\), and have \(\lambda\)-pure dimension greater than 1 for all uncountable \(\lambda\leq |A/tA|\). This result is related to a problem of Neeman about expressing modules as factors of direct sums of smaller modules.