SOME NEW TYPES OF BCK-FILTERS IN BOUNDED BCK-ALGEBRAS

The aim of this work is to investigate and characterize two new types of BCK-filters in bounded BCK-algebras, so we introduce the concepts of EQI-filters and implicative BCK-filters. We clarify the relations between these BCK-filters and show that in PC-lattices, involutory BCK-algebras, commutative BCK-algebras and implicative BCK-algebras, the concepts of BCK-filters, EQI- filters and crazy filters coincide. We also prove that in involutory BCK-algebra every BCK-filter is an implicative BCK-filter if and only if X is an implicative BCK-algebra.