Geodesic
Pseudo-BCK Algebras Derived from Directoids
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 1, p. 125 .

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The aim of this paper is to derive pseudo-BCK algebras from directoids and vice versa. We generalize some results proved by Ivan Chajda et al. in the case of BCK-algebras. We assign to an arbitrary pseudo-BCK algebra a semilattice-like structure and observe that this is the point where directoids are different from the semilattice-like structures. Finally, the relation between commutative deductive systems and derive directoids from a bounded pseudo-BCK(pDN) algebras and a characterization of commutative deductive systems of a bounded pseudo-BCK(pDN) algebra in terms of directoids is discussed.
Classification : 03G25, 06F35, 03F50
Keywords: (commutative) pseudo-BCK algebra, pseudo-BCK lattice, (commutative) deductive system, directoid, semilattice 
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Akbar Rezaei. Pseudo-BCK Algebras Derived from Directoids. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 1, p. 125 . http://geodesic.mathdoc.fr/item/KJM_2022_46_1_a9/