External and weak direct products of 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 UP (BCC)-algebras, we call the external direct product, which is a general concept of the direct product in the sense of Lingcong and Endam, and find the result of the external direct product of special subsets of UP (BCC)-algebras. Also, we introduce the concept of the weak direct product of UP (BCC)-algebras. Finally, we provide several fundamental theorems of (anti-)UP (BCC)-homomorphisms in view of the external direct product UP (BCC)-algebras.