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Full Length Article
International Journal of Neutrosophic Science
Volume 18 , Issue 1, PP: 14-19 , 2022 | Cite this article as | XML | Html |PDF


A Study of Some Neutrosophic Clean Rings

Authors Names :   Mohammad Abobala   1 *     Mikail Bal   2     Ahmed Hatip   3  

1  Affiliation :  Tishreen University, Department of Mathematics, Syria

    Email :  mohammadabobala777@gmail.com

2  Affiliation :  Gaziantep University, Department of Mathematics, Turkey

    Email :  mikailbal46@hotmail.com

3  Affiliation :  Gaziantep University, Department of Mathematics, Turkey

    Email :  kollnaar5@gmail.com

Doi   :   https://doi.org/10.54216/IJNS.180102

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; n-refined neutrosophic ring; classical clean ring; 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., "Reļ¬ned 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.


Cite this Article as :
Mohammad Abobala , Mikail Bal , Ahmed Hatip, A Study of Some Neutrosophic Clean Rings, International Journal of Neutrosophic Science, Vol. 18 , No. 1 , (2022) : 14-19 (Doi   :  https://doi.org/10.54216/IJNS.180102)