Symmetry 2018, 10(8), 321; https://doi.org/10.3390/sym10080321
Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups
Department of Mathematics, Gaziantep University, Gaziantep 27310, Turkey
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Received: 17 July 2018 / Revised: 27 July 2018 / Accepted: 31 July 2018 / Published: 3 August 2018
(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)
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. View Full-TextKeywords:
neutro-monomorphism; neutro-epimorphism; neutro-automorphism; fundamental neutro-homomorphism theorem; first neutro-isomorphism theorem; and second neutro-isomorphism theorem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Çelik, M.; Shalla, M.M.; Olgun, N. Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups. Symmetry 2018, 10, 321.
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