© Hindawi Publishing Corp. ON SOME CLASSES OF BCH-ALGEBRAS

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. 1. Introduction. In 1966, Imai and Iséki introduced two classes of abstract alge-bras, BCK-algebras and BCI-algebras [6, 7]. BCI-algebras are a generalization of BCK-algebras. These algebras have been extensively studied since their introduction. In 1983, Hu and Li [4, 5] introduced the notion of a BCH-algebra, which is a generaliza-tion of the notions of BCK- and BCI-algebras. They have studied a few properties o