Perfect and Local Bounded Equality Algebras

Abstract

In this paper, by considering the notion of bounded equality algebra, we introduce the concepts of perfect, integral and local bounded equality algebras and we state and prove some related results. Specially, we define the notions of some filters such as primary and perfect filters and we get the relation between perfect filters with perfect bounded equality algebras and primary filters in the local bounded equality algebras. Finally, by defining the concepts of radical, locally finite, and peculiar bounded equality algebra, we give a representation for any bounded p-equality and local bounded equality algebras.