1
Islamic University Of Gaza, Palestine
(katyon765@gmail.com)
2
Gaziantep University, Turkey
(mikailbal46@hotmail.com)
3
Malath Aswad, Albaath university, Syria
(malaz.aswad@yahoo.com)
Abstract :
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.
Keywords :
Neutrosophic Ring , Fermat's Diophantine equation , Neutrosophic Integer
References :
[1] Smarandache, F., " A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability", American Research Press. Rehoboth, 2003.
[2] Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, Vol. 43, 2021.
[3] Das, R., Smarandache, F., and Tripathy, B., "Neutrosophic Fuzzy Matrices and Some Algebraic Operations", Neutrosophic Sets and Systems, Vol. 32, pp. 401-409, 2020
[4] Kandasamy, V.W.B., and Smarandache, F., "Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures", Hexis, Phonex, Arizona, 2006.
[5] Agboola, A.A.A., Akinola, A.D., and Oyebola, O.Y., " Neutrosophic Rings I" , International J.Mathcombin, Vol 4,pp 1-14. 2011
[6] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 45, 2021.
[7] Chalapathi, T., and Madhavi, L., "Neutrosophic Boolean Rings", Neutrosophic Sets and Systems, Vol. 33, pp. 57-66. 2020
[8] F. Smarandache, Neutrosophic Theory and Applications, Le Quy Don Technical University, Faculty of Information technology, Hanoi, Vietnam, 17th May 2016.
[9] Abobala, M., "A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences, hindawi, 2021
[10] Abobala, M., and Hatip, A., "An Algebraic Approch To Neutrosophic Euclidean Geometry", Neutrosophic Sets and Systems, Vol. 43, 2021.
[11] Abobala, M., Bal, M., and Hatip, A.," A Review On Recent Advantages In Algebraic Theory Of Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 17, 2021.
[12] Hatip, A., and Olgun, N., "On Refined Neutrosophic R-Module", International Journal of Neutrosophic Science, Vol. 7, pp.87-96. 2020.
[13] Hajjari, A., and Ali, R., " A Contribution To Kothe's Conjecture In Refined Neutrosophic Rings", International Journal of Neutrosophic Science", Vol. 16, 2021.
[14] 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.
[15] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", Neutrosophic Sets and Systems, Vol. 45, 2021.
[16] Wiles, A., "Modular Elliptic Curves and Fermat's Last Theorem", Annals Of Mathematics, 1995.
| Style | # |
|---|---|
| MLA | Katy D. Ahmad, Mikail Bal, Malath Aswad. "A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings." Journal of Neutrosophic and Fuzzy Systems, Vol. 1, No. 2, 2021 ,PP. 55-60 (Doi : https://doi.org/10.54216/JNFS.010201) |
| APA | Katy D. Ahmad, Mikail Bal, Malath Aswad. (2021). A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings. Journal of Journal of Neutrosophic and Fuzzy Systems, 1 ( 2 ), 55-60 (Doi : https://doi.org/10.54216/JNFS.010201) |
| Chicago | Katy D. Ahmad, Mikail Bal, Malath Aswad. "A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings." Journal of Journal of Neutrosophic and Fuzzy Systems, 1 no. 2 (2021): 55-60 (Doi : https://doi.org/10.54216/JNFS.010201) |
| Harvard | Katy D. Ahmad, Mikail Bal, Malath Aswad. (2021). A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings. Journal of Journal of Neutrosophic and Fuzzy Systems, 1 ( 2 ), 55-60 (Doi : https://doi.org/10.54216/JNFS.010201) |
| Vancouver | Katy D. Ahmad, Mikail Bal, Malath Aswad. A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings. Journal of Journal of Neutrosophic and Fuzzy Systems, (2021); 1 ( 2 ): 55-60 (Doi : https://doi.org/10.54216/JNFS.010201) |
| IEEE | Katy D. Ahmad, Mikail Bal, Malath Aswad, A Short Note On The Solutions Of Fermat's Diohantine Equation In Some Neutrosophic Rings, Journal of Journal of Neutrosophic and Fuzzy Systems, Vol. 1 , No. 2 , (2021) : 55-60 (Doi : https://doi.org/10.54216/JNFS.010201) |