External direct products on dual UP (BCC)-algebras

Volume 29, Issue 2, pp 175--191 https://doi.org/10.22436/jmcs.029.02.07

Publication Date: October 20, 2022 Submission Date: June 29, 2022 Revision Date: July 16, 2022 Accteptance Date: July 21, 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. R. Prasertpong - Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan 60000, Thailand. P. Julatha - Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, 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 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.

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Keywords

• BCC-algebra
• dBCC-algebra
• external direct product
• weak direct product
• BCC-homomorphism
• anti-BCC-homomorphism

MSC

•  03G25
•  20K25

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