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Article Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups

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Book Synopsis Article Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups by : Mehmet Çelik

Download or read book Article Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups written by Mehmet Çelik . This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups

Mathematics
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Genre : Mathematics
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Book Synopsis Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups by : Mehmet Çelik

Download or read book Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups written by Mehmet Çelik. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: 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.

COMMUTATIVE NEUTROSOPHIC TRIPLET GROUP AND NEUTRO-HOMOMORPHISM BASIC THEOREM

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Book Synopsis COMMUTATIVE NEUTROSOPHIC TRIPLET GROUP AND NEUTRO-HOMOMORPHISM BASIC THEOREM by : Xiaohong Zhang

Download or read book COMMUTATIVE NEUTROSOPHIC TRIPLET GROUP AND NEUTRO-HOMOMORPHISM BASIC THEOREM written by Xiaohong Zhang. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we further study neutrosophic triplet group. First, to avoid confusion, some new symbols are introduced, and several basic properties of neutrosophic triplet group are rigorously proved (because the original proof is awed), and a result about neutrosophic triplet subgroup is revised. Second, some new properties of commutative neutrosophic triplet group are funded, and a new equivalent relation is established. Third, based on the previous results, the following important propositions are proved: from any commutative neutrosophic triplet group, an Abel group can be constructed; from any commutative neutrosophic triplet group, a BCI-algebra can be constructed. Moreover, some important examples are given. Finally, by using any neutrosophic triplet subgroup of a commutative neutrosophic triplet group, a new congruence relation is established, and then the quotient structure induced by neutrosophic triplet subgroup is constructed and the neutro-homomorphism basic theorem is proved.

New Results on Neutrosophic Extended Triplet Groups Equipped with a Partial Order

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Book Synopsis New Results on Neutrosophic Extended Triplet Groups Equipped with a Partial Order by : Xin Zhou

Download or read book New Results on Neutrosophic Extended Triplet Groups Equipped with a Partial Order written by Xin Zhou. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic extended triplet group (NETG) is a novel algebra structure and it is different from the classical group. The major concern of this paper is to present the concept of a partially ordered neutrosophic extended triplet group (po-NETG), which is a NETG equipped with a partial order that relates to its multiplicative operation, and consider properties and structure features of po-NETGs.

ON NEUTROSOPHIC EXTENDED TRIPLET GROUP ACTION

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Book Synopsis ON NEUTROSOPHIC EXTENDED TRIPLET GROUP ACTION by : Moges Mekonnen Shalla

Download or read book ON NEUTROSOPHIC EXTENDED TRIPLET GROUP ACTION written by Moges Mekonnen Shalla. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: This thesis discusses neutrosophic extended triplet (NET) direct product, semi-direct product and NET group actions. The aim is to give a clear introduction that provides a solid foundation for further studies into the subject. We introduce NET internal and external direct and semi-direct products for NET group by utilizing the notion of NET set theory of Smarandache. We also give examples and discuss their difference with the classical one.

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