On pseudo BE-algebras

In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and preimage of a pseudo filter is also a pseudo filter. Furthermore, the notion 96 R.A. Borzooei, A. Borumand Saeid, A. Rezaei, A. Radfar and ... of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.