Dedekind complete commutative BCK-algebras (Q1583844)

As was shown by the first named author, there is a most general embedding of any commutative BCK-algebra with the relative cancellation property, into a lattice-ordered group. This result provides a useful representation theorem for such BCK-algebras. In this paper the authors characterize various classes of Dedekind-complete BCK algebras, and also generalize Cignoli's theorem on the representation of complete and atomic MV-algebras (= complete atomic bounded commutative BCK algebras).