Direct summands of vector groups (Q1174426)

Cartesian products of subgroups of the rationals are called vector groups. The author deals with the well-known problem whether the class of vector groups is closed under taking direct summands. The answer is yes in some special cases considered in recent years. The author provides a Lemma 2 (p. 207) which serves for the purpose to overcome a defective part in a proof of the problem given in his paper [Pac. J. Math. 117, 379-385 (1985; Zbl 0532.13007)]. Unfortunately, the Lemma is not correct. A counterexample will be published in [\textit{U. Albrecht}, ``A note on Countable Lattices of Types'' (in preparation)].