On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations
On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations

Author: Mohammad Abobala

Publisher: Infinite Study

Published:

Total Pages: 8

ISBN-13:

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This paper studies the problem of determining invertible elements (units) in any n-refined neutrosophic ring. It presents the necessary and sufficient condition for any n-refined neutrosophic element to be invertible, idempotent, and nilpotent. Also, this work introduces some of the elementary algebraic properties of n-refined neutrosophic matrices with a direct application in solving n-refined neutrosophic algebraic equations.

n-Refined Neutrosophic Groups I
n-Refined Neutrosophic Groups I

Author: Mohammad Abobala

Publisher: Infinite Study

Published:

Total Pages: 8

ISBN-13:

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The aim of this paper is to define for the first time the concept of n-refined neutrosophic group. This work is devoted to study some elementary properties of n-refined neutrosophic groups and to establish the algebraic basis of this structure such as n-refined neutrosophic subgroups, n-refined neutrosophic homomorphisms, and n-refined neutrosophic isomorphisms.

n-Refined Neutrosophic Modules
n-Refined Neutrosophic Modules

Author: Hasan Sankari

Publisher: Infinite Study

Published: 2020-10-01

Total Pages: 11

ISBN-13:

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This paper introduces the concept of n-refined neutrosophic module as a new generalization of neutrosophic modules and refined neutrosophic modules respectively and as a new algebraic application of n-refined neutrosophic set. It studies elementary properties of these modules. Also, This work discusses some corresponding concepts such as weak/strong n-refined neutrosophic modules, n-refined neutrosophic homomorphisms, and kernels.

n-Refined Neutrosophic Vector Spaces
n-Refined Neutrosophic Vector Spaces

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 8

ISBN-13:

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This paper introduces the concept of n-refined neutrosophic vector spaces as a generalization of neutrosophic vector spaces, and it studies elementary properties of them. Also, this work discusses some corresponding concepts such as weak/strong n-refined neutrosophic vector spaces, and n-refined neutrosophic homomorphisms.

On Some Neutrosophic Algebraic Equations
On Some Neutrosophic Algebraic Equations

Author: Mohammad Abobala

Publisher: Infinite Study

Published:

Total Pages: 8

ISBN-13:

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This paper is devoted to studying linear equations, and quadratic equations over a neutrosophic field 𝐹(𝐼) and refined neutrosophic field 𝐹(𝐼1,𝐼2). This work introduces a full description of the solution's algorithm in 𝐹(𝐼) and 𝐹(𝐼1,𝐼2), and discusses the solution's algorithm for a linear system of neutrosophic equations over 𝐹(𝐼) and 𝐹(𝐼1,𝐼2) for the first time.

An Introduction to The Symbolic 3-Plithogenic Vector Spaces
An Introduction to The Symbolic 3-Plithogenic Vector Spaces

Author: Rozina Ali

Publisher: Infinite Study

Published: 2023-01-01

Total Pages: 5

ISBN-13:

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The objective of this paper is to define and study for the first time the concept of symbolic 3-plithogenic vector spaces based on symbolic 3-plithogenic sets and classical vector spaces.Also, many related substructures will be defined and handled such as AH-functions, AH-spaces, and symbolic 3-plithogenic basis.

On Some Special Elements in Neutrosophic Rings and Refined Neutrosophic Rings
On Some Special Elements in Neutrosophic Rings and Refined Neutrosophic Rings

Author: Mohammad Abobala

Publisher: Infinite Study

Published:

Total Pages: 8

ISBN-13:

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Idempotent elements in a ring 𝑅 are the elements with the condition 𝒂𝟐=𝒂. This paper introduces the criterion of any element in a refined neutrosophic ring to be idempotent. Also, the concept of symmetric and supersymmetric elements in a neutrosophic ring 𝑅(𝐼), and a refined neutrosophic ring 𝑅(𝐼1,𝐼2) are defined. Also, the invertibility of these elements is discussed.