Abstract
Many algebraic structures can be characterized in terms of some order structure. Among them are lattices, semilattices, boolean algebras, and semi-boolean algebras. In this paper we show that a pBCK-algebra can be characterized in terms of two order relations, one of which also makes it an implicative BCK-algebra. One of these orders is the well-known order for the larger class of BCK-algebras; the other one is a new order we introduce here.
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Guzmán, F. The poset structure of positive implicative BCK-algebras. Algebra Universalis 32, 398–406 (1994). https://doi.org/10.1007/BF01235177
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DOI: https://doi.org/10.1007/BF01235177