%0 Journal Article
%T On Heyting algebras and dual BCK-algebras
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Yon, Y.
%A Kim, K. H.
%D 2012
%\ 04/01/2012
%V 38
%N 1
%P 159-168
%! On Heyting algebras and dual BCK-algebras
%K Heyting semilattice
%K Heyting algebra
%K dual $BCK$-algebra
%R
%X 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.
%U http://bims.iranjournals.ir/article_397_0b7c6a289b3214ec9be3fec521a61f1a.pdf