Extensions in UP-Algebras and Related Properties

Abstract

In this work, we present and explore the idea of extensions of UP-algebras, inspired by similar
constructions in KU-algebras. We begin by recalling fundamental notions related to UP-algebras and proposea
formal definition of an extension in this context. Several illustrative examples are provided to demonstrate the
structure and behavior of these extensions. We examine the relationship between extensions and homomorphic
images, ideals, and congruences, and we establish some necessary and sufficient conditions under which a UPalgebra
extension exists. Furthermore, we compare our results with those obtained in the theory of KU-algebra
extensions to highlight similarities and differences. This study opens new directions in the algebraic analysis
of UP-structures.