Abstract: Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the adjoint semigroups. Moreover,the semigroup differences between positive BCK algebras and implicative BCK algebras are discussed,and some semigroup characterizations of implicative BCK algebras are given.

Key words:  , positive implicative BCK-algebra, implicative BCK-algebra, adjoint semigroup, ideal, order filter