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Commutative pseudo BCK-algebras. (English) Zbl 1212.06049
Summary: Pseudo BCK-algebras generalize the well-known BCK-algebras. A pseudo BCK-algebra is an algebra with two binary operations satisfying some simple axioms which ensure that it is a BCK-algebra whenever these operations coincide. In this paper, we deal with the “pseudo” version of commutative BCK-algebras. We concentrate mainly on commutative pseudo BCK-algebras with the relative cancellation property, which are closely related to lattice-ordered groups.

MSC:
06F35 BCK-algebras, BCI-algebras (aspects of ordered structures)
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