External direct products on dual UP (BCC)-algebras

Abstract

The concept of the direct product of finite family of \(\textit{B}\)-algebras is introduced by Lingcong and Endam [J. A. V. Lingcong, J. C. Endam, Int. J. Algebra, \(\textbf{10}\) (2016), 33--40]. In this paper, we introduce the concept of the direct product of infinite family of BCC-algebras and prove that it is a dual BCC-algebras (dBCC-algebras), we call the external direct product dBCC-algebra induced by BCC-algebras, which is a general concept of the direct product in the sense of Lingcong and Endam. We find the result of the external direct product of special subsets of BCC-algebras. Also, we introduce the concept of the weak direct product dBCC-algebras. Finally, we provide several fundamental theorems of (anti-)BCC-homomorphisms in view of the external direct product dBCC-algebras.