NOTES ON EXTERNAL DIRECT PRODUCTS OF DUAL IUP-ALGEBRAS
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 39
DOI: https://doi.org/10.56827/SEAJMMS.2023.1903.2
Author :
Chatsuda Chanmanee (Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao)
Warud Nakkhasen (Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, THAILAND )
Rukchart Prasertpong (Division of Mathematics and Statistics, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, Nakhon Sawan 60000, THAILAND)
Pongpun Julatha (Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, THAILAND)
Aiyared Iampan (Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao)
Abstract
The concept of the direct product of a finite family of B-algebras is introduced by Lingcong and Endam [15]. In this paper, we introduce the concept of the direct product of an infinite family of IUP-algebras and prove that it is a DIUP-algebra; we call the external direct product DIUP-algebra induced by IUP-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 IUP-algebras. Also, we introduce the concept of the weak direct product DIUP-algebras. Finally, we provide several fundamental theorems of (anti-)IUP-homomorphisms in view of the external direct product DIUP-algebras.
Keywords and Phrases
IUP-algebra, DIUP-algebra, external direct product, weak direct product, IUP homomorphism, anti-IUP-homomorphism.
A.M.S. subject classification
Primary 03G25; Secondary 20K25.
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