# On Heyting algebras and dual BCK-algebras

Document Type : Research Paper

Authors

1 Mokwon University

2 Chungju National University

Abstract

A Heyting algebra is a distributive lattice with implication 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 between 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.

Keywords

### History

• Receive Date: 30 April 2009
• Revise Date: 21 June 2010
• Accept Date: 21 June 2010