Cantor–Bernstein Theorem for Pseudo-BCK-Algebras

We prove that if A and B are orthogonally σ-complete commutative pseudo-BCK-algebras such that A is isomorphic to a direct factor in B, and also B is isomorphic to a direct factor in A, then A and B are isomorphic. As a consequence we obtain previously known results for MV-algebras (by De Simone, Mundici and Navara), pseudo-MV-algebras (by Jakubík) and lattice-ordered groups (again by Jakubík). Supported by the Research and Development Council of the Czech Government, the research project MSM 6198959214.