A new generalization of BE-algebras

In this paper we introduce the notion of PSRU-algebras as a generalization of BE-algebras, we investigate its elementary properties. The aim of this paper is to investigate the concept of filters, left ideals (right ideal, ideal) and fuzzy filters in PSRU-algebras. Moreover, we investigate relationships between left ideals and filters in PSRU-algebras. Furthermore, we characterize filters in terms of fuzzy filters. It is shown that if I be a left ideal of a PSRU-algebra X, then Ix is a left ideal of X for all x∈X