The algebraic structure on the neutrosophic triplet set
Title | The algebraic structure on the neutrosophic triplet set PDF eBook |
Author | S. Suryoto |
Publisher | Infinite Study |
Pages | 7 |
Release | |
Genre | Mathematics |
ISBN |
The notion of the neutrosophic triplet was introduced by Smarandache and Ali. This notion is based on the fundamental law of neutrosophy that for an idea X, we have neutral of X denoted as neut(X) and anti of X denoted as anti(X). This paper studied a neutrosophic triplet set which is a collection of all triple of three elements that satisfy certain properties with some binary operation. Also given some interesting properties related to them. Further, in this paper investigated that from the neutrosophic triplet group can construct a classical group under multiplicative operation for ℤ𝑛 , for some specific n. These neutrosophic triplet groups are built using only modulo integer 2p, with p is an odd prime or Cayley table.
Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets
Title | Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets PDF eBook |
Author | Florentin Smarandache |
Publisher | MDPI |
Pages | 478 |
Release | 2019-04-04 |
Genre | Mathematics |
ISBN | 303897384X |
Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,
Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume II
Title | Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume II PDF eBook |
Author | Florentin Smarandache |
Publisher | Infinite Study |
Pages | 450 |
Release | |
Genre | Mathematics |
ISBN | 3038974765 |
Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,
Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field
Title | Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field PDF eBook |
Author | Mumtaz Ali |
Publisher | Infinite Study |
Pages | 10 |
Release | |
Genre | |
ISBN |
Rings and fields are significant algebraic structures in algebra and both of them are based on the group structure. In this paper, we attempt to extend the notion of a neutrosophic triplet group to a neutrosophic triplet ring and a neutrosophic triplet field.
Study on the Algebraic Structure of Refined Neutrosophic Numbers
Title | Study on the Algebraic Structure of Refined Neutrosophic Numbers PDF eBook |
Author | Qiaoyan Li |
Publisher | Infinite Study |
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.
Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume I
Title | Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume I PDF eBook |
Author | Florentin Smarandache |
Publisher | Infinite Study |
Pages | 480 |
Release | |
Genre | Mathematics |
ISBN | 3038973858 |
Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,
Neutrosophic Triplets in Neutrosophic Rings
Title | Neutrosophic Triplets in Neutrosophic Rings PDF eBook |
Author | Vasantha Kandasamy W. B. |
Publisher | Infinite Study |
Pages | 9 |
Release | |
Genre | Mathematics |
ISBN |
It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition.