Study On The Algebraic Structure Of Refined Neutrosophic Numbers
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| Author | : Qiaoyan Li |
| Publisher | : Infinite Study |
| Total Pages | : 13 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
This paper aims to explore the algebra structure of refined neutrosophic numbers. Firstly, the algebra structure of neutrosophic quadruple numbers on a general field is studied. Secondly, The addition operator and multiplication operator on refined neutrosophic numbers are proposed and the algebra structure is discussed. We reveal that the set of neutrosophic refined numbers with an additive operation is an abelian group and the set of neutrosophic refined numbers with a multiplication operation is a neutrosophic extended triplet group. Moreover, algorithms for solving the neutral element and opposite elements of each refined neutrosophic number are given.
| Author | : Mohammad Abobala |
| Publisher | : Infinite Study |
| Total Pages | : 8 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Florentin Smarandache |
| Publisher | : Infinite Study |
| Total Pages | : 6 |
| Release | : |
| Genre | : |
| ISBN | : |
In this paper, we make a short history about: the neutrosophic set, neutrosophic numerical components and neutrosophic literal components, neutrosophic numbers, neutrosophic intervals, neutrosophic hypercomplex numbers of dimension n, and elementary neutrosophic algebraic structures.
| Author | : Florentin Smarandache |
| Publisher | : Infinite Study |
| Total Pages | : 7 |
| Release | : |
| Genre | : |
| ISBN | : |
This paper is an improvement of our paper β(t, i, f)-Neutrosophic Structuresβ [1], where we introduced for the first time a new type of structures, called (t, i, f)Neutrosophic Structures, presented from a neutrosophic logic perspective, and we showed particular cases of such structures in geometry and in algebra.
| Author | : Hasan Sankari |
| Publisher | : Infinite Study |
| Total Pages | : 11 |
| Release | : 2020-10-01 |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Mohammad Abobala |
| Publisher | : Infinite Study |
| Total Pages | : 8 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
Idempotent elements in a ring π
are the elements with the condition ππ=π. 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 π
(πΌ), and a refined neutrosophic ring π
(πΌ1,πΌ2) are defined. Also, the invertibility of these elements is discussed.
| Author | : Adel Mohammad Al-Odhari |
| Publisher | : Infinite Study |
| Total Pages | : 12 |
| Release | : 2024-01-01 |
| Genre | : Mathematics |
| ISBN | : |
This paper aims to make a valuable contribution to the field of neutrosophic determinants and their properties. By utilizing neutrosophic real numbers in the form of a+bI, we provide an alternative approach to recent research on determinants conducted between 2020 and 2023. Our goal is to expand the scope of academic content being developed in the theory of neutrosophic linear algebra. Additionally, we seek to complement our work on some algebraic structures of neutrosophic matrices.
| Author | : Mohammad Abobala |
| Publisher | : Infinite Study |
| Total Pages | : 7 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Florentin Smarandache |
| Publisher | : Infinite Study |
| Total Pages | : 8 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
The aim of this paper is to introduce the concept of n-refined neutrosophic ring as a generalization of refined neutrosophic ring. Also, wepresent concept of n-refined polynomial ring. We study some basic concepts related to these rings such as AH-subrings, AH-ideals, AH-factors, and AH-homomorphisms.
| Author | : Florentin Smarandache |
| Publisher | : Infinite Study |
| Total Pages | : 9 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
The aim of this paper is to introduce the concept of n-refined neutrosophic ring as a generalization of refined neutrosophic ring. Also, wepresent concept of n-refined polynomial ring. We study some basic concepts related to these rings such as AH-subrings, AH-ideals, AH-factors, and AH-homomorphisms.
