ON Class of Subalgebras of Bounded BCK-Algebras

In this paper, for any 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 2 X. Using these subalgebras, we characterize the involutive BCK-algebras, and give a necessary and suffcient 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.