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Lattice operation in BCK-algebras. (English) Zbl 0555.03030

In this paper we consider BCK-algebras with additional lattice operations. We show that BCK-algebras as this constitute varieties, i.e. equationally defined classes. This result is rather unexpected, since as it is known BCK-algebras do not form a variety. Further we prove some theorems about various possibilities of embedding of BCK-algebras into BCK-algebras with additional lattice operations.

MSC:

03G25 Other algebras related to logic
06A12 Semilattices
08B99 Varieties
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