Implicative Pseudo-BCK Algebras and Implicative Pseudo-Filters of Pseudo-BCK Algebras

Abstract

The notions of 1-type implicative pseudo-BCK algebra and 2-type implicative pseudo-BCK algebra are introduced, and the relations among 1-type (2-type) implicative pseudo-BCK algebras and implicative BCK-algebras. Moreover, the notion of implicative pseudo-filter is introduced, and a characterization of bounded 1-type (2-type) implicative pseudo-BCK algebra is obtained by implicative pseudo-filter.