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On Heyting algebras and dual BCK-algebras

Y. Yon, K. H. Kim

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Abstract

Abstract. A Heyting algebra is a distributive lattice with im-plication and a dual BCK-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras be-tween dual BCK-algebras. We define notions of i-invariant and m-invariant on dual BCK-semilattices and prove that a Heyting semilattice is equivalent to an i-invariant and m-invariant dual BCK-semilattices, and show that a commutative Heyting algebra is equivalent to a bounded implicative dual BCK-algebra. 1.

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Abstract. A Heyting algebra is a distributive lattice with im-plication and a dual BCK-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras be-tween dual BCK-algebras. We define notions of i-invariant and m-invariant on dual BCK-semilattices and prove that a Heyting semilattice is equivalent to an i-invariant and m-invariant dual BCK-semilattices, and show that a commutative Heyting algebra is equivalent to a bounded implicative dual BCK-algebra. 1.

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Available abstract

Abstract. A Heyting algebra is a distributive lattice with im-plication and a dual BCK-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras be-tween dual BCK-algebras. We define notions of i-invariant and m-invariant on dual BCK-semilattices and prove that a Heyting semilattice is equivalent to an i-invariant and m-invariant dual BCK-semilattices, and show that a commutative Heyting algebra is equivalent to a bounded implicative dual BCK-algebra. 1.

Key concepts: Heyting algebra, Mathematics, Semilattice, Distributive lattice, Dual (grammatical number), Pure mathematics, Algebra over a field, Commutative property

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