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 On commutative weak BCK-algebras

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The class of weak BCK-algebras is obtained by weakening one of standard BCK axioms. It is known that every weak BCK-algebra is completely determined by the structure of its initial segments. We review several classes of commutative weak BCK-algebras, show that they are varieties, and characterize the initial segments of algebras in each of these classes as lattices equipped with a suitable kind of complementation. In particular, commutative weak BCK-algebras are just those meet semilattices with the least element in which all initial segments are non-distributive de Morgan lattices.

Author: Janis Cirulis

Source: https://archive.org/

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