On some classes of BCH-algebras (Q5932790)

m5mmary: BCH-algebras are a generalization of BCI-algebras. 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.