A New Approach on Derivations of Hyperlattices

The main goal of this paper is to reintroduce and study the concept of derivation on hyperlattices. We introduce the notion of joinitive and strong-joinitive derivation and study some of their properties and relationship with isotone and contractive derivations on hyperlattices. Moreover, we study some properties of the fixed set of principal derivation and investigate the relationship between prime ideals and derivations in hyperlattice. Finally, we prove that the set of all principal derivations on a bounded hyperlattice L is isomorphic to L and we investigate the structure of the set of fixed set of principal derivations and established an isomorphism between this set and that of all the principal derivations on a distributive hyperlattice.