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Journal articles on the topic 'Neutrosophic triplet ring'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Merkepci, Hamiyet, and Katy D. Ahmad. "On the Conditions of Imperfect Neutrosophic Duplets and Imperfect Neutrosophic Triplets." Galoitica: Journal of Mathematical Structures and Applications 2, no. 2 (2022): 08–13. http://dx.doi.org/10.54216/gjmsa.020201.

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In any neutrosophic ring R(I), an imperfect neutrosophic duplet consists of two elements x,y with a condition xy=yx=x and an imperfect neutrosophic triplet consists of three elements x,y,z with condition xy=yx=x,yz=zy=z,and xz=zx=y. The objective of this paper is to determine the necessary and sufficient conditions for neutrosophic duplets and triplets in any neutrosophic ring R(I), and to determine all triplets in Z(I).

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2

Ali, Mumtaz, Florentin Smarandache, and Mohsin Khan. "Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field." Mathematics 6, no. 4 (2018): 46. http://dx.doi.org/10.3390/math6040046.

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3

Çeven, Yılmaz, and Florentin Smarandache. "Correction: Ali, M., et al. Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field. Mathematics 2018, 6, 46." Mathematics 7, no. 6 (2019): 565. http://dx.doi.org/10.3390/math7060565.

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4

Zhang, Xiaohong, Wangtao Yuan, Mingming Chen, and Florentin Smarandache. "A Kind of Variation Symmetry: Tarski Associative Groupoids (TA-Groupoids) and Tarski Associative Neutrosophic Extended Triplet Groupoids (TA-NET-Groupoids)." Symmetry 12, no. 5 (2020): 714. http://dx.doi.org/10.3390/sym12050714.

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The associative law reflects symmetry of operation, and other various variation associative laws reflect some generalized symmetries. In this paper, based on numerous literature and related topics such as function equation, non-associative groupoid and non-associative ring, we have introduced a new concept of Tarski associative groupoid (or transposition associative groupoid (TA-groupoid)), presented extensive examples, obtained basic properties and structural characteristics, and discussed the relationships among few non-associative groupoids. Moreover, we proposed a new concept of Tarski ass

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5

Merkepci, Hamiyet, and Ahmed Hatip. "Algorithms for Computing Pythagoras Triples and 4-Tiples in Some Neutrosophic Commutative Rings." International Journal of Neutrosophic Science 20, no. 3 (2023): 107–14. http://dx.doi.org/10.54216/ijns.200310.

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This paper is dedicated to study the number theoretical Pythagoras triples\4-tiples problem in several kinds of neutrosophic algebraic systems, where it finds an algorithm to find Pythagoras triples\4-tiples in commutative neutrosophic rings and refined neutrosophic rings too. Besides, the necessary and sufficient condition for a triple\4-tiple to be Pythagoras triple\4-tiple (quadruples) is obtained and proven in term of theorems. In addition, many numerical examples will be illustrated.

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6

Kandasamy W. B., Vasantha, Ilanthenral Kandasamy, and Florentin Smarandache. "Neutrosophic Triplets in Neutrosophic Rings." Mathematics 7, no. 6 (2019): 563. http://dx.doi.org/10.3390/math7060563.

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The neutrosophic triplets in neutrosophic rings ⟨ Q ∪ I ⟩ and ⟨ R ∪ I ⟩ are investigated in this paper. However, non-trivial neutrosophic triplets are not found in ⟨ Z ∪ I ⟩ . In the neutrosophic ring of integers Z ∖ { 0 , 1 } , no element has inverse in Z. 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.

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7

Josef, Josef, and Ahmad Khaldi. "The Mathematical Formulas of 2-Cyclic Refined Duplets and Triplets." Galoitica: Journal of Mathematical Structures and Applications 11, no. 2 (2024): 44–49. https://doi.org/10.54216/gjmsa.0110206.

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This work is dedicated to studying the problem of computing 2-cyclic refined neutrosophic duplets and triplets in the 2-cyclic refined neutrosophic ring of real numbers, where we present four different formulas that describe all possible duplets in this extended ring. Also, we present four different formulas for the computation of related triplets in the same ring.

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8

ÇEVEN, Yilmaz, and Doğukan OZAN. "Neutrosophic triplets in some neutrosophic rings." Cumhuriyet Science Journal 41, no. 3 (2020): 612–16. http://dx.doi.org/10.17776/csj.685154.

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9

Sankari, Hasan, and Mohammad Abobala. "On The Classification of The Group of Units of Rational and Real 2-Cyclic Refined Neutrosophic Rings." Neutrosophic Sets and Systems 54 (April 11, 2023): 89–100. https://doi.org/10.5281/zenodo.7817657.

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The objective of this paper is to solve two open problems about the group of units of some 2-cyclic refined neutrosophic rings asked by Sadiq. Where it provides a classification theorem for these rings, and uses this classification property to give a full answer of these open questions. Also, this work presents a novel algorithm to find all imperfect neutrosophic duplets and triplets in many numerical 2-cyclic refined neutrosophic rings by using the classification isomorphisms.

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10

Alfahal, Abuobida M. A., Yaser A. Alhasan, Raja A. Abdulfatah, and Rozina Ali. "On the Solutions of Fermat's Diophantine Equation in 2-cyclic Refined Neutrosophic Ring of Integers." International Journal of Neutrosophic Science 20, no. 3 (2023): 08–14. http://dx.doi.org/10.54216/ijns.200301.

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The Diophantine equation X^n+Y^n=Z^n is called the Fermat's Diophantine equation. Its solutions are called general Fermat's triples.The aim of this paper is to study the solutions of Fermat's Diophantine equation in the 2-cyclic refined neutrosophic ring of integers, where we determine all possible solutions of this Diophantine equation, as well as, the special case of Pythagoras triples.

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11

Bal, Mikail, Katy D. Ahmad, Arwa A. Hajjari, and Rozina Ali. "The Structure Of Imperfect Triplets In Several Refined Neutrosophic Rings." Journal of Neutrosophic and Fuzzy Systems, 2022, 21–30. http://dx.doi.org/10.54216/jnfs.020103.

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This paper solves the imperfect triplets problem in refined neutrosophic rings, where it presents the necessary and sufficient conditions for a triple (x,y,z) to be an imperfect triplet in any refined neutrosophic ring. Also, this work introduces a full description of the structure of imperfect triplets in numerical refined neutrosophic rings such as refined neutrosophic ring of integers Z(I1,I2) , refined neutrosophic ring of rationales Q(I1,I2), and refined neutrosophic ring or real numbers (R(I1,I2).

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12

Mumtaz, Ali, Smarandache Florentin, and Khan Mohsin. "Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field." September 7, 2018. https://doi.org/10.5281/zenodo.1411300.

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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. We introduce a neutrosophic triplet ring and study some of its basic properties. Further, we define the zero divisor, neutrosophic triplet subring, neutrosophic triplet ideal, nilpotent integral neutrosophic triplet domain, and neutrosophic triplet ring homomorphism. Finally, we introduce a neutrosophic triplet field.

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13

Ali, Mumtaz, and M. Khan. "Study on the development of neutrosophic triplet ring and neutrosophic triplet field." January 8, 2014. https://doi.org/10.5281/zenodo.234094.

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14

Florentin, Smarandache, and Ali Mumtaz. "Neutrosophic Triplet Group (revisited)." June 12, 2019. https://doi.org/10.5281/zenodo.3244162.

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We have introduced for the first time the notion of neutrosophic triplet since 2014, which has the form (x, neut(x), anti(x)) with respect to a given binary well-defined law, where neut(x) is the neutral of x, and anti(x) is the opposite of x. Then we define the neutrosophic triplet group (2016), prove several theorems about it, and give some examples. This paper is an improvement and a development of our 2016 published paper. Groups are the most fundamental and rich algebraic structure with respect to some binary operation in the study of algebra. In this paper, for the first time, we introdu

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15

Xiaohong, Zhang, Ma Zhirou, and Yuan Wangtao. "Cyclic Associative Groupoids (CA-Groupoids) and Cyclic Associative Neutrosophic Extended Triplet Groupoids (CA-NET-Groupoids)." October 20, 2019. https://doi.org/10.5281/zenodo.3514387.

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Group is the basic algebraic structure describing symmetry based on associative law. In order to express more general symmetry (or variation symmetry), the concept of group is generalized in various ways, for examples, regular semigroups, generalized groups, neutrosophic extended triplet groups and AG-groupoids. In this paper, based on the law of cyclic association and the background of non-associative ring, left weakly Novikov algebra and CA-AG-groupoid, a new concept of cyclic associative groupoid (CA-groupoid) is firstly proposed, and some examples and basic properties are presented. Moreov

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16

Ahmad, Katy D., Mikail Bal, and Malath Aswad. "A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings." Journal of Neutrosophic and Fuzzy Systems, 2021, 55–60. http://dx.doi.org/10.54216/jnfs.010201.

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This paper is dedicated to study the concept of Fermat's triples in rings. Also, it determines the possible Fermat's triples in the neutrosophic ring of integers Z(I). Also, it discussed these triples in several finite commutative rings such as Zn.

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17

Sarkis, Maretta. "On The Solutions Of Fermat's Diophantine Equation In 3-refined Neutrosophic Ring of Integers." Neoma Journal Of Mathematics and Computer Science 1, no. 1 (2023). https://doi.org/10.5281/zenodo.7953660.

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This work is dedicated to study the Fermat's Diophantine equation over the 3-refined neutrosophic ring of integers, where we provide an algorithm to find all triples that represent solutions of this non-linear Diophantine equation.

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