Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups PDF Download
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Author: Mehmet Çelik Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 14
Book Description
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.
Author: Mehmet Çelik Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 14
Book Description
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.
Author: Xiaohong Zhang Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 23
Book Description
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.
Author: Moges Mekonnen Shalla Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 18
Book Description
The object of this article is mainly to discuss the notion of neutrosophic extended triplet direct product (NETDP) and neutrosophic extended triplet semi-direct product (NETS-DP) of NET group. The purpose is to give a clear introduction that allows a solid foundation for additional studies into the field. We introduce neutrosophic extended triplet internal direct product (NETIDP) and neutrosophic extended triplet external direct products (NETEDP) of NET group. Then, we define NET internal and external semi-direct products for NET group by utilizing the notion of NET set theory of Smarandache. Moreover, some results related to NETDP and NETS-DPs are obtained.
Author: Xiaoying Wu Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 12
Book Description
In this paper, some new properties of Abel Grassmann‘s Neutrosophic Extended Triplet Loop (AG-NET-Loop) were further studied. The following important results were proved: (1) an AG-NET-Loop is weakly commutative if, and only if, it is a commutative neutrosophic extended triplet (NETG); (2) every AG-NET-Loop is the disjoint union of its maximal subgroups. At the same time, the new notion of Abel Grassmann’s (l, l)-Loop (AG-(l, l)-Loop), which is the Abel-Grassmann’s groupoid with the local left identity and local left inverse, were introduced. The strong AG-(l, l)-Loops were systematically analyzed, and the following decomposition theorem was proved: every strong AG-(l, l)-Loop is the disjoint union of its maximal sub-AG-groups.
Author: Moges Mekonnen Shalla Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 26
Book Description
The aim of this article is mainly to discuss the neutrosophic extended triplet (NET) group actions and Burnside’s lemma of NET group. We introduce NET orbits, stabilizers, conjugates and NET group action. Then, we give and proof the Orbit stabilizer formula for NET group by utilizing the notion of NET set theory. Moreover, some results related to NET group action, and Burnside’s lemma are obtained.
Author: Moges Mekonnen Shalla Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 76
Book Description
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.
Author: Florentin Smarandache Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 264
Book Description
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.
Author: Florentin Smarandache Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 262
Book Description
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.