ON SOME CLASSES OF BCH-ALGEBRASMUHA

ON SOME CLASSES OF BCH-ALGEBRAS
MUHAMMAD ANWAR CHAUDHRY and HAFIZ FAKHAR-UD-DIN
Abstract. The concept of a BCH-algebra is a generalization of the concept of a BCI-algebra.
It is shown that weakly commutative BCH-algebras are weakly commutative BCI-algebras.
Moreover, the concepts of weakly positive implicative and weakly implicative BCH-algebras
are defined and it is shown that every weakly implicative BCH-algebra is a weakly positive
implicative BCH-algebra. The weakly positive implicative BCH-algebras are characterized
with the help of their self maps. Two open problems are posed.
2000 Mathematics Subject Classification. Primary 06F35, 03G25.