Abstract

BI-algebra was introduced in 2017 by A. Borumand Saeid, H. S. Kim and A. Rezaei. Then this class of logical algebras was the focus of many researchers. In this paper, we register an additional property of ideals in right distributive BI-algebras. Then, in this paper we discuss the following two things: the definition of the concept of atoms in right distributive BI-algebras and the registration of many properties of such a designed concept of atoms. In addition to the previous one, the paper designs an extension of the right distributive BI-algebra A = (A, ·, 0) by adding one element w /∈ A such that w is an atom in A.