Cantor-Bernstein theorem for pseudo-BCK-algebras (Q2426163)

The main scope of this paper is to prove the following Cantor-Bernstein-type theorem for pseudo BCK-algebras: If \(A\) and \(B\) are orthogonally \(\sigma\)-complete commutative pseudo BCK algebras such that \(A\) is isomorphic to a direct factor in \(B\), and \(B\) is also isomorphic to a direct factor in \(A\), then \(A\) and \(B\) are isomorphic. As a consequence, the author obtains previously known results for MV-algebras, pseudo MV-algebras and lattice-ordered groups.