NOTES ON EXTERNAL DIRECT PRODUCTS OF DUAL IUP-ALGEBRAS

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 66

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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