External and weak direct products of UP (BCC)-algebras

Volume 29, Issue 1, pp 90--105 http://dx.doi.org/10.22436/jmcs.029.01.08

Publication Date: August 24, 2022 Submission Date: May 02, 2022 Revision Date: July 05, 2022 Accteptance Date: July 07, 2022

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Authors

C. Chanmanee - Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. R. Chinram - Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. N. Phrommarat - Department of Mathematics, Faculty of Science and Technology, Chiang Rai Rajabhat University, Chiang Rai 57100, Thailand. P. Julatha - Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand. N. Lekkoksung - Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000, Thailand. A. Iampan - Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand.

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.

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Keywords

• UP-algebra
• BCC-algebra
• external direct product
• weak direct product
• UP (BCC)-homomorphism
• anti-UP (BCC)-homomorphism

MSC

•  03G25
•  20K25

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