On a representable class of separated lattice EQ-algebras

El-Zekey, Moataz; Khalaf, Mahmoud

doi:10.21608/jbes.2020.371141

On a representable class of separated lattice EQ-algebras

Document Type : Original Article

Authors

Moataz El-Zekey ¹
Mahmoud Khalaf ²

¹ Department of Engineering Mathematics, Physics and Science, Faculty of Engineering, Damietta University, New Damietta, 34517

² Department of basic Science, Faculty of Engineering, Benha University, Egypt

10.21608/jbes.2020.371141

Abstract

In this paper, we introduce and study a class of separated lattice EQ-algebras that may be represented as subalgebras of
products of linearly ordered ones. Such algebras are called representable. Namely, we enrich separated lattice EQ-algebras
with a unary operation (the so called Baaz delta), fulfilling some additional assumptions. The resulting algebras are called
ℓEQΔ
s
-algebras. One of the main results of this paper is to characterize the class of representable ℓEQΔ
s
-algebras. We also
supply a number of useful results, leading to this characterization.