Fundamental BCC-algebras

Abstract

In this paper, we consider the notions of  BCC-algebras and  hyper BCC-algebras, give some related results, introduce the relation $\beta$ on  hyper BCC-algebras and let $\beta^*$ be the transitive closure of $\beta$.   Then  by considering the concept of strongly regular equivalence relation (fundamental  relation) $\beta^*$ on  hyper BCC-algebras, we define the notion of fundamental BCC-algebra and we prove that any countable   BCC-algebra is a fundamental BCC-algebra.