Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401On Heyting algebras and dual BCK-algebras159168397ENY.YonMokwon UniversityK. H.KimChungju National UniversityJournal Article20090430A 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.http://bims.iranjournals.ir/article_397_0b7c6a289b3214ec9be3fec521a61f1a.pdf