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Pseudo BCK-semilattices

Kuhr J.

Demonstratio Mathematica

2007

Vol. 40, nr 3

495-516

Pseudo BCK-algebras are algebras (A,approaches 1) of type (2, 2, 0) which generalize BCK-algebras in such a way that if the operations-› and ->coincide then (A,-›, 1) is a BCK-algebra. They can be also viewed as {-›,->, 1}-subreducts of non-commutative integral residuated lattices. In the paper, we study pseudo BCK-algebras whose underlying posets are semilattices or lattices; we call them pseudo BCK-join-semilattices, pseudo BCK-meet-semilattices and pseudo BCK-lattices, respectively. After describing their congruence properties we deal mainly with prime deductive systems of pseudo BCK-join-semilattices.