PI-LATTICES IN BOUNDED BCK-ALGEBRAS

In this paper, we define a concept of a PI-lattice in bounded BCK-lattices. It is proved that PI-lattices include some current lattices such as bounded involuntory BCK-algebras, bounded implicative BCK- algebras (boolean lattices) and positive implicative BCK-lattices with condition S, that these are lattices in bounded BCK-algebras. Some important properties of this lattice are characterized. Moreover it is proved each PI- lattice is a distributive lattice. In this research it is denoted that the relation between these lattices in bounded BCK-lattices, that is showed by a figure in the end of this paper.