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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
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