On Class of Subalgebras of Bounded BCK-algebras

Abstract

In this paper, to each two elements y; u of a BCK-algebra X, we assign a subset of X, denoted by Sy(u), and investigate some related properties. We show that Sy(u) is a subalgebra of X for all y; u in X. Using these subalgebras, we characterize the involitive BCK-algebras, and give a necessary and suucient condition for a bounded BCK-algebra to be a commutative BCK-chain. Finally, we show that the set of all subalgebras Sy(u) forms a bounded distributive lattice.