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
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