External Direct Product JU-Algebras

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DOI: https://doi.org/10.28924/2291-8639-22-2024-183
Published: Oct 15, 2024
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Chatsuda Chanmanee, Pongpun Julatha, Warud Nakkhasen, Rukchart Prasertpong, Aiyared Iampan, External Direct Product JU-Algebras, Int. J. Anal. Appl., 22 (2024), 183.

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Chatsuda Chanmanee, Pongpun Julatha, Warud Nakkhasen, Rukchart Prasertpong, Aiyared Iampan

Abstract

Lingcong and Endam introduced the idea of the direct product of a finite family of B-algebras. In this paper, we introduce the concept of the direct product of an infinite family of JU-algebras, which we call the external direct product. This is a general concept of the direct product in the sense of Lingcong and Endam. The result is based on different types of subsets of JU-algebras. These include JU-subalgebras, JU-ideals, p-ideals, t-ideals, strong JU-ideals, JU-filters, comparative JU-filters, and implicative JU-filters. Also, we introduce the concept of the weak direct product of JU-algebras. Finally, we provide several fundamental theorems of (anti-)JU-homomorphisms in view of the external direct product JU-algebras.

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