Volume 18 , Issue 1 , PP: 14-19, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
Mohammad Abobala 1 * , Mikail Bal 2 , Ahmed Hatip 3
Doi: https://doi.org/10.54216/IJNS.180102
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).
refined neutrosophic ring , , n-refined , neutrosophic ring , classical clean ring , , neutrosophic clean ring
[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.
