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Keywords:
BCK-algebras; deductive system; irreducible deductive system; Heyting algebras; annihilators
BCK-algebras; deductive system; irreducible deductive system; Heyting algebras; annihilators
Summary:
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].
References:
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