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 of a bounded bck-algebra. to do this, first, we define the operations ⋏,⋎ and ⊔ on bck-algebras and we study some algebraic properties of them. also, for a bounded bck-algebra a we define the zariski topology on spec(a) and the induced topology τa,max(a) on m ax(a). we prove (m ax(a), τa,max(a) ) is a compact topological space if a has glivenko property. using the open and the closed sets of m ax(a), we define a congruence relation on a bounded bck-algebra a and we show la, the quotient set, is a bounded distributive lattice. we call this lattice the belluce lattice associated with a. finally, we show (la, pa) is a reticulation of a (in the sense of definition 5.1) and the lattices la and sa are isomorphic.