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.
Highlights
Groups are finite or infinite set of elements which are vital to modern algebra equipped with an operation that satisfies the four basic axioms of closure, associativity, the identity property, and the inverse property
Firstly introduced by “Galois” [2], with the study of polynomials has applications in physics, chemistry, and computer science, and puzzles like the Rubik’s cube as it may be expressed utilizing group theory. Homomorphism is both a monomorphism and an epimorphism maintaining a map between two algebraic structures of the same type and isomorphism is a bijective homomorphism defined as a morphism, which has an inverse that is morphism
The most common use of neutro-homomorphisms and neutro-isomorphisms in this study is to deal with homomorphism theorems which allow for the identification of some neutrosophic triplet quotient objects with certain other neutrosophic triplet subgroups, and so on
Summary
Groups are finite or infinite set of elements which are vital to modern algebra equipped with an operation (such as multiplication, addition, or composition) that satisfies the four basic axioms of closure, associativity, the identity property, and the inverse property. Firstly introduced by “Galois” [2], with the study of polynomials has applications in physics, chemistry, and computer science, and puzzles like the Rubik’s cube as it may be expressed utilizing group theory Homomorphism is both a monomorphism and an epimorphism maintaining a map between two algebraic structures of the same type (such as two groups, two rings, two fields, two vector spaces) and isomorphism is a bijective homomorphism defined as a morphism, which has an inverse that is morphism. Similarity measures of bipolar neutrosophic sets and single valued triangular neutrosophic numbers and their appliance to multi-attribute group decision making investigated in [19,20].
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