On commutative CI-algebras

Abstract

$\mathrm{Cl}$-algebra is a generalization of $\mathrm{BE}$-algebra. The concept of Commutative $\mathrm{BE}$-algebra was first introduced by A. Walendziak. B. L. Meng applied the same definition in $\mathrm{Cl}$-algebras and established that any commutative $\mathrm{Cl}$-algebra is a $\mathrm{BE} /$ dual $\mathrm{BCK}$-algebra. In this paper we continue to study commutative $\mathrm{Cl}$-algebras and try to establish some properties in some specific $\mathrm{Cl}$-algebras.