Geodesic
Deductive systems of BCK-algebras
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 27-32.

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In this paper we shall give some results on irreducible deductive systems in BCK-algebras and we shall prove that the set of all deductive systems of a BCK-algebra is a Heyting algebra. As a consequence of this result we shall show that the annihilator $F^{\ast }$ of a deductive system $F$ is the the pseudocomplement of $F$. These results are more general than that the similar results given by M. Kondo in [7].
Classification : 03F35, 03G25, 06D20, 06F35
Keywords: BCK-algebras; deductive system; irreducible deductive system; Heyting algebras; annihilators 
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Celani, Sergio A. Deductive systems of BCK-algebras. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 27-32. http://geodesic.mathdoc.fr/item/AUPO_2004__43_1_a2/