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International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
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Continuous publication

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Open access journal. All articles are freely available online with no APC.

International Journal of Neutrosophic Science
Full Length Article

Volume 18Issue 1PP: 14-19 • 2022

A Study of Some Neutrosophic Clean Rings

Mohammad Abobala 1* ,
Mikail Bal 2 ,
Ahmed Hatip 2
1Tishreen University, Department of Mathematics, Syria
2Gaziantep University, Department of Mathematics, Turkey
* Corresponding Author.
verified

Open Access & Copyright

© 2022 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

June 15, 2021 Accepted: Jan 02, 2022

Abstract

The objective of this paper is to introduce a necessary and sufficient condition for a neutrosophic ring to be clean. This work proves the equivalence between case of classical clean ring R and the corresponding neutrosophic ring R(I), refined neutrosophic ring R(I_1,I_2 ), and n-refined neutrosophic ring R_n (I).

Keywords

refined neutrosophic ring &nbsp n-refined&nbsp neutrosophic ring classical clean ring &nbsp neutrosophic clean ring

References

[1] Kandasamy, V.W.B., and Smarandache, F., "Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures", Hexis, Phonex, Arizona 2006.

[2] Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic Equations, Journal Of Mathematics, Hindawi, 2021

[3] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", NSS, Vol. 45, 2021.

[4] Abobala, M., "Neutrosophic Real Inner Product Spaces", NSS, vol. 43, 2021.

[5] Abobala, M., and Hatip, A., "An Algebraic Approach to Neutrosophic Euclidean Geometry", NSS, Vol. 43, 2021.

[6] Adeleke, E.O., Agboola, A.A.A.,and Smarandache, F., "Refined Neutrosophic Rings I", IJNS, Vol. 2(2), pp. 77-81, 2020. 

[7] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021

[8] Olgun, N., Hatip, A., Bal, M., and Abobala, M., " A Novel Approach To Necessary and Sufficient Conditions For The Diagonalization of Refined Neutrosophic Matrices", IJNS, Vol. 16, pp. 72-79, 2021.

[9] Suryoto, H., and Uidjiani, T., " On Clean Neutrosophic Rings", IOP Conference Series, Journal of Physics, Conf. Series 1217, 2019.

[10] Abobala, M., "On Some Special Elements In Neutrosophic Rings and Refined Neutrosophic Rings", Journal of New Theory, vol. 33, 2020.

[11] Abobala, M., Hatip, A., and Bal, M., " A Review On Recent Advantages In Algebraic Theory Of Neutrosophic Matrices", IJNS, Vol.17, 2021. 

[12] Abobala, M., "A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences, hindawi, 2021

[13] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", NSS, Vol. 45, 2021.

 

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Abobala, Mohammad, Bal, Mikail, Hatip, Ahmed. "A Study of Some Neutrosophic Clean Rings." International Journal of Neutrosophic Science, vol. Volume 18, no. Issue 1, 2022, pp. 14-19. DOI: https://doi.org/10.54216/IJNS.180102
Abobala, M., Bal, M., Hatip, A. (2022). A Study of Some Neutrosophic Clean Rings. International Journal of Neutrosophic Science, Volume 18(Issue 1), 14-19. DOI: https://doi.org/10.54216/IJNS.180102
Abobala, Mohammad, Bal, Mikail, Hatip, Ahmed. "A Study of Some Neutrosophic Clean Rings." International Journal of Neutrosophic Science Volume 18, no. Issue 1 (2022): 14-19. DOI: https://doi.org/10.54216/IJNS.180102
Abobala, M., Bal, M., Hatip, A. (2022) 'A Study of Some Neutrosophic Clean Rings', International Journal of Neutrosophic Science, Volume 18(Issue 1), pp. 14-19. DOI: https://doi.org/10.54216/IJNS.180102
Abobala M, Bal M, Hatip A. A Study of Some Neutrosophic Clean Rings. International Journal of Neutrosophic Science. 2022;Volume 18(Issue 1):14-19. DOI: https://doi.org/10.54216/IJNS.180102
M. Abobala, M. Bal, A. Hatip, "A Study of Some Neutrosophic Clean Rings," International Journal of Neutrosophic Science, vol. Volume 18, no. Issue 1, pp. 14-19, 2022. DOI: https://doi.org/10.54216/IJNS.180102
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