Some New Kinds of BCK-Filters in Bounded BCK-Algebras

Abstract

This paper investigates and characterizes some new types of BCK-filters in bounded BCK-algebras. We introduce the notions of EQI-filters, implicative BCK-filters, and commutative BCK-filters. We clarify the relationships among these filters and prove that every implicative BCK-filter is a commutative BCK-filter and every commutative BCK-filter is an EQI-filter, although the converses do not hold in general. We also study these filters in several important subclasses of BCK-algebras. For instance, in involutory BCK-algebras, the notions of EQI-filters, implicative BCK-filters, and commutative BCK-filters coincide, whereas they are distinct in general.