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Algebraic structures derived from BCK-algebras. (English) Zbl 1135.03349
Summary: Commutative BCK-algebras can be viewed as semilattices whose sections have antitone involutions and it is known that bounded commutative BCK-algebras are equivalent to MV-algebras. In the first part of this paper we assign to an arbitrary BCK-algebra a semilattice-like structure every section of which possesses a certain antitone mapping. The remaining part is devoted to algebras of the MV-language $$\{\oplus,\neg,0\}$$ which are defined on bounded BCK-algebras in the same way as MV-algebras.

##### MSC:
 03G25 Other algebras related to logic 06D35 MV-algebras 06F35 BCK-algebras, BCI-algebras (aspects of ordered structures)
##### Keywords:
BCK-algebra; MV-algebra; semilattice; antitone mapping