We introduce a relative cancellation property for
commutative BCK-algebras and we study the problem of
embedding of commutative BCK-algebras into Abelian lattice
ordered groups. We show that if a BCK-algebra is not upwards
directed, then we cannot use the method of Wyler and Baer.
Anyway, supposing either union property or unitarily
extendibility, we can present the embedding of such a
BCK-algebra into the positive cone of an Abelian lattice
ordered group with universal property. Finally, some
interesting examples are presented.
