Independent UP-algebras

Abstract

In this paper, we introduce the concept of a new algebraic structure: independent UP-algebras (in short, IUP-algebras), which is independent of UP-algebras. We also introduce the concepts of IUP-subalgebras, IUP-filters, IUP-ideals, and strong IUP-ideals of IUP-algebras and investigate their properties and relationships. Finally, we discuss the concept of homomorphisms between IUP-algebras and also study the direct and inverse images of four special subsets.