Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups

Abstract

In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related.

Keywords

• neutro-monomorphism
• neutro-epimorphism
• neutro-automorphism
• fundamental neutro-homomorphism theorem
• first neutro-isomorphism theorem
• and second neutro-isomorphism theorem