1
Imam Kadhum College, Iraq
(basheerabdalrida66n@gmail.com)
2
Islamic University Of Gaza, Palestine
(katyon765@gmail.com)
3
Cairo University, Egypt
(rozyyy123n@gmail.com)
Abstract :
The objective of this paper is to present a new class of Diophantine equations derived from the group of units problem of n-cyclic refined neutrosophic rings of integers by using homomorphisms between these rings and a finite Cartesian product ring of Z with itself.
Also, this work provides many examples about this class and its solvability as a new application of neutrosophic algebraic structures in number theory.
Keywords :
n-cyclic refined neutrosophic ring; n-cyclic refined neutrosophic integer; group of units
References :
[1] M. Abobala. n-Cyclic Refined Neutrosophic Algebraic Systems Of Sub-Indeterminacies, An
Application To Rings and Modules, International Journal of Neutrosophic Science, Vol. 12, 2020. pp.
81-95.
[2] E. Adeleke. A. Agboola. , and F. Smarandache. Refined Neutrosophic Rings I. IJNS, 2020.
[3] V. Kandasamy and F. Smarandache. Some Neutrosophic Algebraic Structures and Neutrosophic NAlgebraic
Structures", Hexis, Phonex, Arizona, 2006.
[4] Smarandache, F., " n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in
Physics, 143-146, Vol. 4, 2013.
[5] Abobala, M., Hatip, A., Bal, M.," A Study Of Some Neutrosophic Clean Rings", International Journal
of neutrosophic science, 2022.
[6] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic
Rings", Neutrosophic Sets and Systems, Vol. 45, 2021.
[7] Olgun, N., Hatip, A., Bal, M., and Abobala, M., " A Novel Approach To Necessary and Sufficient
Conditions For The Diagonalization of Refined Neutrosophic Matrices", International Journal of
neutrosophic Science, Vol. 16, pp. 72-79, 2021.
[8] Agboola, A.A.A., "On Refined Neutrosophic Algebraic Structures," Neutrosophic Sets and Systems,
Vol.10, pp. 99-101. 2015.
[9] Abobala, M., Hatip, A., and Bal, M., " A Review On Recent Advantages In Algebraic Theory Of
Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol.17, 2021.
[10] Abobala, M., and Hatip, A., "An Algebraic Approach To Neutrosophic Euclidean Geometry",
Neutrosophic Sets and Systems, Vol. 43, 2021.
[11] Hatip, A., and Olgun, N., "On Refined Neutrosophic R-Module", International Journal of Neutrosophic
Science, Vol. 7, pp.87-96. 2020.
[12] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory",
Neutrosophic sets and systems, Vol. 45, 2021.
[13] Abobala, M., Ziena, M., Doewes, R., and Hussien, Z., "The Representation Of Refined Neutrosophic
Matrices By Refined Neutrosophic Linear Functions", International Journal Of Neutrosophic Science,
2022.
[14] Sadiq, B., " A Contribution To The Group Of Units' Problem In Some 2-Cyclic Refined Neutrosophic
Rings", IJNS, 2022.
[15] Suresh, R., and S. Palaniammal,. "Neutrosophic Weakly Generalized open and Closed Sets",
Neutrosophic Sets and Systems, Vol. 33, pp. 67-77,. 2020.
[16] Aswad, M., " A Study Of neutrosophic Differential Equation By using A Neutrosophic Thick
Function", neutrosophic knowledge, Vol. 1, 2020.
[17] Milles, S, Barakat, M, and Latrech, A., " Completeness and Compactness In Standard Single Valued
neutrosophic Metric Spaces", International Journal of Neutrosophic Science, Vol.12, 2021.
[18] Smarandache, F., "Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets", Inter. J. Pure
Appl. Math., pp. 287-297. 2005.
[19] Agboola, A.A.A,. and Akinleye, S.A,. "Neutrosophic Vector Spaces", Neutrosophic Sets and Systems,
Vol. 4, pp. 9-17, 2014.
[20] Abobala, M., Bal, M., Aswad, M., "A Short Note On Some Novel Applications of Semi Module
Homomorphisms", International Journal of neutrosophic science, 2022.
[21] Von Shtawzen, O., " Conjectures For Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic
Refined Integers", Journal Of Neutrosophic And Fuzzy Systems, Vol.3, 2022.
| Style | # |
|---|---|
| MLA | A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. "Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers." Galoitica: Journal of Mathematical Structures and Applications, Vol. 1, No. 1, 2022 ,PP. 36-41 (Doi : https://doi.org/10.54216/GJMSA.010103) |
| APA | A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. (2022). Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers. Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 ( 1 ), 36-41 (Doi : https://doi.org/10.54216/GJMSA.010103) |
| Chicago | A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. "Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers." Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 no. 1 (2022): 36-41 (Doi : https://doi.org/10.54216/GJMSA.010103) |
| Harvard | A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. (2022). Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers. Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 ( 1 ), 36-41 (Doi : https://doi.org/10.54216/GJMSA.010103) |
| Vancouver | A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2022); 1 ( 1 ): 36-41 (Doi : https://doi.org/10.54216/GJMSA.010103) |
| IEEE | A. Alrida Basheer, Katy D. Ahmad, Rozina Ali, Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 1 , No. 1 , (2022) : 36-41 (Doi : https://doi.org/10.54216/GJMSA.010103) |