Neutrosophic κ-Structures in Ordered Semigroups

Muhiuddin, G.; Porselvi, K.; Elavarasan, B.; Al-Kadi, Deena

doi:10.32604/cmes.2022.018615

Cited by 3 publications

(1 citation statement)

References 15 publications

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“…In [13], B. Elavarasan et al investigated various properties of neutrosophic N-ideals in semigroups. In [14], Muhiuddin et al defined neutrosophic N-ideals and neutrosophic N-interior ideals in ordered semigroups and studied their properties. They also used neutrosophic N-ideals and neutrosophic N-interior ideals to describe ordered semigroups.…”

Section: Introductionmentioning

confidence: 99%

Neutrosophic 𝔑-Structures in Semimodules over Semirings

Muhiuddin,

Abughazalah,

Elavarasan

et al. 2023

Symmetry

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The study of symmetry is a fascinating and unifying subject that connects various areas of mathematics in the twenty-first century. Algebraic structures offer a framework for comprehending the symmetries of geometric objects in pure mathematics. This paper introduces new concepts in algebraic structures, concentrating on semimodules over semirings and analysing the neutrosophic structure in this context. We explore the properties of neutrosophic subsemimodules and neutrosophic ideals after defining them. We discuss, utilizing neutrosophic products, the representations of neutrosophic ideals and subsemimodules, as well as the relationship between neutrosophic products and intersections. Finally, we derive equivalent criteria in terms of neutrosophic structures for a semiring to be fully idempotent.

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Section: Introductionmentioning

confidence: 99%

Neutrosophic 𝔑-Structures in Semimodules over Semirings

Muhiuddin,

Abughazalah,

Elavarasan

et al. 2023

Symmetry

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𝒩-Structures Applied to Commutative Ideals of BCI-Algebras

2022

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The study of symmetry is one of the most important and beautiful themes uniting various areas of contemporary arithmetic. Algebraic structures are useful structures in pure mathematics for learning a geometrical object’s symmetries. In order to provide a mathematical tool for dealing with negative information, a negative-valued function came into existence along with N-structures. In the present analysis, the notion of N-structures is applied to the ideals, especially the commutative ideals of BCI-algebras. Firstly, several properties of N-subalgebras and N-ideals in BCI-algebras are investigated. Furthermore, the notion of a commutative N-ideal is defined, and related properties are investigated. In addition, useful characterizations of commutative N-ideals are established. A condition for a closed N-ideal to be a commutative N-ideal is provided. Finally, it is proved that in a commutative BCI-algebra, every closed N-ideal is a commutative N-ideal.

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Crossing cubic Lie algebras

Al-Masarwah,

Kdaisat,

Abuqamar

et al. 2024

MATH

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<p>An interval-valued fuzziness structure is an effective approach addressing ambiguity and for expressing people's hesitation in everyday situations. An $ \mathcal{N} $-structure is a novel technique for solving practical problems. This is beneficial for resolving a variety of issues, and a lot of progress is being made right now. In order to develop crossing cubic structures ($ \mathcal{CCS}s $), Jun et al. amalgamate interval-valued fuzziness and $ \mathcal{N} $-structures. In this manuscript, our main contribution is to originate the concepts of crossing cubic ($ \mathcal{CC} $) Lie algebra, $ \mathcal{CC} $ Lie sub-algebra, ideal, and homomorphism. We investigate some properties of these concepts. In a Lie algebra, the construction of a quotient Lie algebra via the $ \mathcal{CC} $ Lie ideal is provided. Furthermore, the $ \mathcal{CC} $ isomorphism theorems are presented.</p>

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Neutrosophic κ-Structures in Ordered Semigroups

Cited by 3 publications

References 15 publications

Neutrosophic 𝔑-Structures in Semimodules over Semirings

Neutrosophic 𝔑-Structures in Semimodules over Semirings

𝒩-Structures Applied to Commutative Ideals of BCI-Algebras

Crossing cubic Lie algebras

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