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.