## Weakly positive implicative and weakly implicative BCI-algebras.(English)Zbl 0702.06014

It is shown that no proper classes of positive implicative, implicative, commutative or bounded BCI-algebras exist. That is, such BCI-algebras are BCK-algebras of the corresponding type. In the paper the notions of positive implicativeness, implicativeness and commutativity are generalized in such a way that the respective generalized class contains all BCK-algebras of the corresponding type as well as proper BCI- algebras.
Reviewer: M.Pałasiński

### MSC:

 06F35 BCK-algebras, BCI-algebras

### Keywords:

weakly implicative BCI-algebras; proper BCI-algebras