TY - JOUR
ID - 397
TI - On Heyting algebras and dual BCK-algebras
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Yon, Y.
AU - Kim, K. H.
AD - Mokwon University
AD - Chungju National University
Y1 - 2012
PY - 2012
VL - 38
IS - 1
SP - 159
EP - 168
KW - Heyting semilattice
KW - Heyting algebra
KW - dual $BCK$-algebra
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_397.html
L1 - http://bims.iranjournals.ir/article_397_0b7c6a289b3214ec9be3fec521a61f1a.pdf
ER -