e-Subalgebras and e-Homomorphisms of PGK2-Algebras - Abd El-Mohsen Badawy; Essam El-Seidy; Mohiedeen Ahmed; Ahmed Gaber (Journal of Mathematics)
This paper is devoted for three main purposes. First, subalgebras, e-subalgebras of a principal generalized K2-algebra (PGK2-algebra), and their associated principal generalized K2-triples are studied. We prove that every GM-subalgebra, GK-subalgebra, De Morgan subalgebra, Kleene subalgebra, and Boolean subalgebra of a generalized K2-algebra is a principal subalgebra. Examples are provided to determine all different types of certain principal generalized K2-algebras. Second, the completion problem concerning principal generalized K2-triples is solved and an example is given to explain how to apply it. Finally, we define homomorphisms and e-homomorphisms between two principal generalized K2-algebras. We show that every e-homomorphism determines a triple homomorphism of principal generalized K2-triples and every triple homomorphism uniquely determines an e-homomorphism of principal generalized K2-algebras.