Abstract:

As a generalization of the self-distributive BE-algebra, the concept of JNB-algebras is introduced in 2025 by Y. B. Jun et al., and its basic properties are investigated. In this short note, we show that in every JNB-algebra \( A = (A, \ast, 1) \), the natural congruence relation \( \equiv \) can be determined such that the factor-algebra \( A/\equiv \) is an aBE-algebra, that is, it is a JNB-algebra that additionally satisfies the conditions \( (Ex) \) and \( (An) \).