Distributive pseudo BE-algebras

In this paper, we introduce the notion of distributive pseudo BE-algebra and show that the related relation defined on this structure is transitive and prove that every pseudo upper set is a pseudo filter. Also, the pseudo filter generated by a set is define and show that the set of all pseudo filters is distributive complete lattice but it is not complemented. the notion of prime and irreducible subset and prove that every irreducible subset is prime.