### Journals Information

**
Mathematics and Statistics Vol. 11(1), pp. 206 - 212 DOI: 10.13189/ms.2023.110124 Reprint (PDF) (271Kb) **

## A Note on External Direct Products of BP-algebras

**Chatsuda Chanmanee ^{1}, Rukchart Prasertpong ^{2}, Pongpun Julatha ^{3}, U. V. Kalyani ^{4}, T. Eswarlal ^{4}, Aiyared Iampan ^{1}^{,*}**

^{1}Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand

^{2}Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan 60000, Thailand

^{3}Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand

^{4}Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, AP, India

**ABSTRACT**

The notion of BP-algebras was introduced by Ahn and Han [2] in 2013, which is related to several classes of algebra. It has been examined by several researchers. In the group, the concept of the direct product (DP) [21] was initially developed and given some features. Then, other algebraic structures are subjected to DP groups. Lingcong and Endam [16] examined the idea of the DP of (0-commutative) B-algebras and B-homomorphisms in 2016 and discovered several related features, one of which is a DP of two Balgebras that is a B-algebra. Later on, the concept of the DP of B-algebra was expanded to include finite family B-algebra, and some of the connected issues were researched. In this work, the external direct product (EDP), a general concept of the DP, is established, and the results of the EDP for certain subsets of BP-algebras are determined. In addition, we define the weak direct product (WDP) of BP-algebras. In light of the EDP BP-algebras, we conclude by presenting numerous essential theorems of (anti-)BP-homomorphisms.

**KEYWORDS**

BP-algebra, External Direct Product, Weak Direct Product, BP-homomorphism, Anti-BP-homomorphism

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Chatsuda Chanmanee , Rukchart Prasertpong , Pongpun Julatha , U. V. Kalyani , T. Eswarlal , Aiyared Iampan , "A Note on External Direct Products of BP-algebras," Mathematics and Statistics, Vol. 11, No. 1, pp. 206 - 212, 2023. DOI: 10.13189/ms.2023.110124.

(b). APA Format:

Chatsuda Chanmanee , Rukchart Prasertpong , Pongpun Julatha , U. V. Kalyani , T. Eswarlal , Aiyared Iampan (2023). A Note on External Direct Products of BP-algebras. Mathematics and Statistics, 11(1), 206 - 212. DOI: 10.13189/ms.2023.110124.