The Belluce lattice associated with a bounded BCK -algebra

In this paper, we introduce the notions of Belluce lattice associated with a bounded $BCK$-algebra and reticulation $BCK$-algebra. To do this, first, define operations $curlywedge ,$ $curlyvee $ $sqcup on $BCK$-algebras study some algebraic properties them. Also, for $A$ Zariski topology Spec(A)$ induced $tau _{A,Max(A)}$ $Max(A)$. We prove $(Max(A),tau_{A,Max(A)})$ is compact topological space if has Glivenko property. Using open closed sets $Max(A)$, congruence relation show $L_{A}$, quotient set, distributive lattice. call $A.$ Finally, $(L_{A},p_{A})$ (in sense Definition ref{d7}) lattices $L_{A}$ $S_{A}$ are isomorphic.