Hyper equality algebras

Abstract

In this paper, we introduce a new structure, called hyper equality algebras which are a generalization of equality algebras, and investigate some related properties. Then we define (weak, strong) hyper filters and (weak, strong) hyper deductive systems, and give relations between them. Moreover we discuss relations between hyper equality algebras and other hyper structures, such as hyper EQ-algebras, hyper BCK-algebras and weak hyper residuated lattices. Finally, we also obtain quotient hyper equality algebras via regular hyper congruence relations.