Pseudo Commutative Double Basic Algebras

Abstract

In this paper, we study the concept of pseudo commutative double basic algebras and investigate some related results. We prove that there are relations among pseudo commutative double basic algebras and other logical algebras such as pseudo hoops, pseudo BCK-algebras and double MV-algebras. We obtain a close relation between pseudo commutative double basic algebras and pseudo residuted l-groupoids. Then we investigate the properties of the boolean center of pseudo commutative double basic algebras and we use the boolean elements to define and study algebras on subintervals of pseudo commutative double basic algebras.