Inverse Properties in Neutrosophic Triplet Loop and Their Application to Cryptography

Jaiyeola, Temitope Gbolahan; Smarandache, Florentín

doi:10.3390/a11030032

Cited by 9 publications

(8 citation statements)

References 18 publications

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“…For discussions of results on neutrosophic triplet groups, neutrosophic quadruples, and neutrosophic duplets of algebraic structures, as well as new applications of neutrosophy, see Jaiyéo . lá and Smarandache [29]. Jaiyéo .…”

Section: Neutrosophic Triplet Groupmentioning

confidence: 99%

Some Results on Neutrosophic Triplet Group and Their Applications

Jaiyeola

Smarandache

2018

Symmetry

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This article is based on new developments on a neutrosophic triplet group (NTG) and applications earlier introduced in 2016 by Smarandache and Ali. NTG sprang up from neutrosophic triplet set X: a collection of triplets (b, neut(b), anti(b)) for an b ∈ X that obeys certain axioms (existence of neutral(s) and opposite(s)). Some results that are true in classical groups were investigated in NTG and were shown to be either universally true in NTG or true in some peculiar types of NTG. Distinguishing features between an NTG and some other algebraic structures such as: generalized group (GG), quasigroup, loop and group were investigated. Some neutrosophic triplet subgroups (NTSGs) of a neutrosophic triplet group were studied. In particular, for any arbitrarily fixed a ∈ X, the subsets X a = {b ∈ X : neut(b) = neut(a)} and ker f a = {b ∈ X| f (b) = neut(f (a))} of X, where f : X → Y is a neutrosophic triplet group homomorphism, were shown to be NTSG and normal NTSG, respectively. Both X a and ker f a were shown to be a-normal NTSGs and found to partition X. Consequently, a Lagrange-like formula was found for a finite NTG X; |X| = ∑ a∈X [X a : ker f a ]| ker f a | based on the fact that | ker f a | |X a |. The first isomorphism theorem X/ ker f ∼ = Im f was established for NTGs. Using an arbitrary non-abelian NTG X and its NTSG X a , a Bol structure was constructed. Applications of the neutrosophic triplet set, and our results on NTG in relation to management and sports, are highlighted and discussed.

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Section: Neutrosophic Triplet Groupmentioning

confidence: 99%

Some Results on Neutrosophic Triplet Group and Their Applications

Jaiyeola

Smarandache

2018

Symmetry

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“…New results and developments on neutrosophic triplet groups and neutrosophic triplet loop have been reported by Zhang et al [18,20,21], and Smarandache and Jaiyéo . lá [22,23].…”

Section: Bci-algebras As a Quasi Neutrosophic Triplet Loopmentioning

confidence: 99%

On the Classification of Bol-Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop (Fenyves BCI-Algebras)

Jaiyeola¹,

Ilojide

Olatinwo

et al. 2018

Symmetry

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In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative. The 46 associative algebras are shown to be Boolean groups. Moreover, necessary and sufficient conditions for 13 non-associative algebras to be associative are also obtained: p-semisimplicity is found to be necessary and sufficient for a F 3 , F 5 , F 42 and F 55 algebras to be associative while quasi-associativity is found to be necessary and sufficient for F 19 , F 52 , F 56 and F 59 algebras to be associative. Two pairs of the 14 non-associative algebras are found to be equivalent to associativity ( F 52 and F 55 , and F 55 and F 59 ). Every BCI-algebra is naturally an F 54 BCI-algebra. The work is concluded with recommendations based on comparison between the behaviour of identities of Bol-Moufang (Fenyves’ identities) in quasigroups and loops and their behaviour in BCI-algebra. It is concluded that results of this work are an initiation into the study of the classification of finite Fenyves’ quasi neutrosophic triplet loops (FQNTLs) just like various types of finite loops have been classified. This research work has opened a new area of research finding in BCI-algebras, vis-a-vis the emergence of 540 varieties of Bol-Moufang type quasi neutrosophic triplet loops. A ‘Cycle of Algebraic Structures’ which portrays this fact is provided.

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“…And in [30], sorts of general neutrosophic triplet structures were pointed out, and their basic properties were investigated. For the structure of NETG, some research papers are published with a series of results [31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

The Decomposition Theorems of AG-Neutrosophic Extended Triplet Loops and Strong AG-(l, l)-Loops

Zhang

2019

Mathematics

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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.

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Inverse Properties in Neutrosophic Triplet Loop and Their Application to Cryptography

Cited by 9 publications

References 18 publications

Some Results on Neutrosophic Triplet Group and Their Applications

Some Results on Neutrosophic Triplet Group and Their Applications

On the Classification of Bol-Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop (Fenyves BCI-Algebras)

The Decomposition Theorems of AG-Neutrosophic Extended Triplet Loops and Strong AG-(l, l)-Loops

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