Very true operators on equality algebras

摘要

In this paper, we introduce the concept of very true operators on equality algebras and investigate some related properties of such operators. As an application of properties of very true operators on equality algebras, we give a characterization of prelinear equality algebras, and discuss the relation between very true operator and internal state operator on equality algebras. Moreover, we put forth the notion of very true filter on equality algebras and obtain some important results. In particular, using very true filter, we characterize the simple very true equality algebras and establish the uniform structures on very true equality algebras.