Open problems on implicative pseudo-filters and boolean filters

Abstract

We proposed the relation between implicative pseudo-filter and Boolean filter of pseudo BCK algebras with condition (pP) or bounded pseudo BCK algebras with condition (pP) and partly solved open problems that "In pseudo BCK algebra or bounded pseudo BCK algebra, is the notion of implicative pseudo-filter equivalent to the notion of Boolean filter?" and "A pseudo BCK algebra is an implicative pseudo BCK algebras if and only if every pseudo-filters of it is Boolean filter (or implicative pseudo-filters).