EQ-algebras with Modal Operators

The main goal of this paper is to investigate modal operators on EQ-algebras. To begin with, we introduce the concept of modal EQ-algebras, that is, EQ-algebras equipped with modal operators. Moreover, we study some basic properties of modal EQ-algebras, and we obtain that modal operators are closure operators on EQ-algebras and vice verse. Furthermore, we introduce modal filters(prefilters) and modal congruences of modal EQ-algebras. We show that there is a one-to-one correspondence between modal filters and modal congruences on good modal EQalgebras. Finally, we give a characterization for minimal modal prime prefilters and characterize the representable good modal EQ-algebras via minimal modal prime prefilters.