scholarly journals On Homomorphism Theorem for Perfect Neutrosophic Extended Triplet Groups

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 237 ◽  
Author(s):  
Xiaohong Zhang ◽  
Xiaoyan Mao ◽  
Florentin Smarandache ◽  
Choonkil Park
Keyword(s):  
Homomorphism Theorem

Some homomorphism theorems of neutrosophic extended triplet group (NETG) are proved in the paper [Fundamental homomorphism theorems for neutrosophic extended triplet groups, Symmetry 2018, 10(8), 321; doi:10.3390/sym10080321]. These results are revised in this paper. First, several counterexamples are given to show that some results in the above paper are not true. Second, two new notions of normal NT-subgroup and complete normal NT-subgroup in neutrosophic extended triplet groups are introduced, and their properties are investigated. Third, a new concept of perfect neutrosophic extended triplet group is proposed, and the basic homomorphism theorem of perfect neutrosophic extended triplet groups is established.

Generalising and dualising the third list-homomorphism theorem

2011 ◽  
Vol 46 (9) ◽  
pp. 385-391
Author(s):  
Shin-Cheng Mu ◽  
Akimasa Morihata
Keyword(s):  
The Third ◽  
Homomorphism Theorem

scholarly journals Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 321 ◽  
Author(s):  
Mehmet Çelik ◽  
Moges Shalla ◽  
Necati Olgun
Keyword(s):  
Group Theory ◽  
Significant Role ◽  
Classical Group ◽  
Algebraic Structures ◽  
Algebraic Systems ◽  
Homomorphism Theorem ◽  
Special Cases ◽  
Isomorphism Theorems

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.

Extensions of I-Bisimple Semigroups

1967 ◽  
Vol 19 ◽  
pp. 419-426 ◽  
Author(s):  
R. J. Warne
Keyword(s):  
Homomorphic Image ◽  
Natural Order ◽  
Isomorphism Theorem ◽  
Maximal Group ◽  
Homomorphism Theorem ◽  
Complete Determination ◽  
Explicit Determination ◽  
Usual Order

A bisimple semigroup S is called I-bisimple if Es, the set of idempotents of S, with its natural order is order-isomorphic to I, the set of integers, under the reverse of the usual order. In (9), the author completely determined the structure of I-bisimple semigroups mod groups; in this paper, he also gave an isomorphism theorem, a homomorphism theorem, an explicit determination of the maximal group homomorphic image, and a complete determination of the congruences for these semigroups.

Visualizing the Group Homomorphism Theorem

1995 ◽  
Vol 26 (2) ◽  
pp. 143
Author(s):  
Robert C. Moore
Keyword(s):  
Group Homomorphism ◽  
Homomorphism Theorem

scholarly journals A homomorphism theorem for projective planes

1971 ◽  
Vol 4 (2) ◽  
pp. 155-158 ◽  
Author(s):  
Don Row
Keyword(s):  
Projective Plane ◽  
Homomorphic Image ◽  
Inverse Image ◽  
Projective Planes ◽  
Homomorphism Theorem ◽  
Central Collineations

We prove that a non-degenerate homomorphic image of a projective plane is determined to within isomorphism by the inverse image of any one point. An application gives conditions for the preservation of central collineations by a homomorphism.

On Finite NeutroGroups of Type-NG[1,2,4]

2020 ◽  
pp. 84-95
Author(s):  
admin admin ◽  
Keyword(s):  
Identity Element ◽  
The Other ◽  
Classical Groups ◽  
Basic Properties ◽  
Homomorphism Theorem ◽  
Different Types ◽  
Lagrange's Theorem

The NeutroGroups as alternatives to the classical groups are of different types with different algebraic prop- erties. In this paper, we are going to study a class of NeutroGroups of type-NG[1,2,4]. In this class of Neu- troGroups, the closure law, the axiom of associativity and existence of inverse are taking to be either partially true or partially false for some elements; while the existence of identity element and axiom of commutativity are taking to be totally true for all the elements. Several examples of NeutroGroups of type-NG[1,2,4] are presented along with their basic properties. It is shown that Lagrange’s theorem holds for some NeutroSub- groups of a NeutroGroup and failed to hold for some NeutroSubgroups of the same NeutroGroup. It is also shown that the union of two NeutroSubgroups of a NeutroGroup can be a NeutroSubgroup even if one is not contained in the other; and that the intersection of two NeutroSubgroups may not be a NeutroSubgroup. The concepts of NeutroQuotientGroups and NeutroGroupHomomorphisms are presented and studied. It is shown that the fundamental homomorphism theorem of the classical groups is holding in the class of NeutroGroups of type-NG[1,2,4].

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