A Review on Recent Advantages in Algebraic Theory of Neutrosophic Matrices

Abobala, Mohammad; Bal, Mikail; Hatip, Ahmed

doi:10.54216/ijns.170105

Cited by 6 publications

(5 citation statements)

References 1 publication

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“…Symbolic 2-plithogenic matrices were defined and studied in [14]; these matrices consist of symbolic 2-plithogenic real entries. These matrices are recognized as a similar structure of refined neutrosophic matrices and structures [15][16][17][18][19][20][21][22][23][24]. In matrix theory, it is very important to deal with the exponents of matrices and their related problems, such as how to diagonalize a matrix, and how to compute eigenvalues and eigenvectors.…”

Section: Introductionmentioning

confidence: 99%

On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

Merkepci

2023

Symmetry

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Symbolic n-plithogenic sets are considered to be modern concepts that carry within their framework both an algebraic and logical structure. The concept of symbolic n-plithogenic algebraic rings is considered to be a novel generalization of classical algebraic rings with many symmetric properties. These structures can be written as linear combinations of many symmetric elements taken from other classical algebraic structures, where the square symbolic k-plithogenic real matrices are square matrices with real symbolic k-plithogenic entries. In this research, we will find easy-to-use algorithms for calculating the determinant of a symbolic 3-plithogenic/4-plithogenic matrix, and for finding its inverse based on its classical components, and even for diagonalizing matrices of these types. On the other hand, we will present a new algorithm for calculating the eigenvalues and eigenvectors associated with matrices of these types. Also, the exponent of symbolic 3-plithogenic and 4-plithogenic real matrices will be presented, with many examples to clarify the novelty of this work.

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Section: Introductionmentioning

confidence: 99%

On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

Merkepci

2023

Symmetry

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“…Neutrosophic number theory was introduced in [4]. Also, in [5] and [6], the authors examined some properties of neutrosophic integers. Studies on neutrophic integers have inspired many articles.…”

Section: Introductionmentioning

confidence: 99%

“…Definition 2.5[6] Let 𝑎 + 𝑏𝐼 ∈ 𝑍[𝐼] . 𝑎 + 𝑏𝐼 is a positive neutrosophic number if and only if 𝑎 > 0, 𝑎 + 𝑏𝐼 > 0.Definition 2.6 [4] Let 𝛼 = 𝛼 1 + 𝛼 2 𝐼 ∈ 𝑍[𝐼] .…”

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confidence: 99%

The Greatest Common Divisors and The Least Common Multiples in Neutrosophic Integers

Çeven,

Çetin

2023

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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As a continuation of previous studies, we give some results about the neutrosophic integers theory. We first stated that the neutrosophic real numbers are not closed according to the division operation. Later, we gave divisibility properties of neutrosophic integers. We have given properties such as the greatest common divisor for two neutrosophic integers being positive and unique. Then, we gave the Euclid’s Theorem, Bezout’s Theorem for neutrosophic ingers set Z[I]. It is known that these concepts are important for number theory in integers set Z. Finally, it is defined the least common multiple for neutrosophic integers. Finally, a theorem is given which enables one to easily find the least common multiple of neutrosophic integers and after a conclusion about the sign of the product of two neutrosophic integers, a theorem is given that shows the relationship of between the greatest common divisor with the least common multiple

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“…For more information about neutrosophic algebra [5][6][7][8][9][10] or four way Turiyam ring author can refer to [16][17][18][19] for basic understanding of mathematical proof [20].…”

Section: Introductionmentioning

confidence: 99%

Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers

Shtawzen¹

2022

JNFS

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A Review on Recent Advantages in Algebraic Theory of Neutrosophic Matrices

Abstract: This work is dedicated to give the reader a wide review for recent advantages in the algebraic study of neutrosophic matrices, refined neutrosophic matrices, and n-refined neutrosophic matrices.

Cited by 6 publications

References 1 publication

On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

The Greatest Common Divisors and The Least Common Multiples in Neutrosophic Integers

Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers

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