Boolean and Central Elements and Cantor-Bernstein Theorem in Bounded Pseudo-BCK-Algebras?
Boolean and central elements of bounded pseudo-BCK-algebras are studied. Boolean elements form a largest boolean subalgebra and include central elements, which correspond one-one to direct product decompositions. Further, a Cantor-Bernstein type theorem is proved, generalizing similar results for σ-complete MV-algebras and orthogonally σ-complete pseudo-MV-algebras.
Keywords: Pseudo-BCK-algebra, boolean element, central element, direct product decomposition, Cantor-Bernstein theorem.
Mathematics Subject Classification: 03G25, 06D35, 06F35.