Galoitica: Journal of Mathematical Structures and Applications
Journal DOI
2834-5568ISSN (Online)
Volume 9 , Issue 1 , PP: 45-51, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
P. Prabakaran 1 *
Doi: https://doi.org/10.54216/GJMSA.090105
A ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize this argument to neutrosophic structure. We introduce the structure of nil-clean neutrosophic ring and some of its elementary properties are presented. Also, we have found the equivalence between classical nil-clean ring R and the corresponding neutrosophic ring R(I), refined neutrosophic ring R(I1, I2), and n-refined neutrosophic ring Rn(I).
Clean ring , nil-clean ring , neutrosophic ring , refined neutrosophic ring , clean neutrosophic ring , nil-clean neutrosophic ring.
[1] M. Abobala, On Some Special Elements In Neutrosophic Rings and Refined Neutrosophic Rings, Journal of New Theory, vol. 33, 2020.
[2] M. Abobala, A Study of Nil Ideals and Kothey Conjecture in Neutrosophic Rings, International Journal of Mathematics and Mathematical Sciences, vol. 1, 2021.
[3] M. Abobala, M. Bal and A. Hatip, A Study Of Some Neutrosophic Clean Rings, International Journal of Neutrosophic Science (IJNS) Vol. 18, No. 01, pp. 14-19, 2022
[4] A. A. A. Agboola, A. D. Akinola, and O. Y. Oyebola, Neutrosophic Rings I, International J.Math combin, Vol 4, pp. 1-14, 2011.
[5] A. A. A. Agboola , E. O. Adeleke and S. A, Akinleye, Neutrosophic Ring II, International, J. Math. Combin. 2(1), 2012.
[6] M. Abobala, On Some Special Substructures of Neutrosophic Rings and Their Properties, International Journal of Neutrosophic Science”, Vol. 4, pp. 72-81, 2020.
[7] E.O. Adeleke, A.A.A. Agboola and F. Smarandache, Refined Neutrosophic Rings I, International Journal of Neutrosophic Science, Vol 2 , pp 77-81, 2020.
[8] E.O. Adeleke, A.A.A. Agboola and F. Smarandache, ”Refined Neutrosophic Rings II”, International Journal of Neutrosophic Science, Vol 2, pp 89-94, 2020.
[9] D.D. Anderson, V.P. Camilo, Commutative rings whose elements are a sum of a unit and idempotent, Comm. Algebra, 30 (2002), pp. 3327-3336.
[10] S. Breaz, G. Calugareanu, P. Danchev, T. Micu, Nil-clean matrix rings, Linear Algebra Appl., 439 (2013), pp. 3115-3119.
[11] T. Chalabathi and K. Kumar, Neutrosophic Units of Neutrosophic Rings and Fields, Neutrosophic Sets and Systems, vol 21, pp 5-9, 2018.
[12] A.J. Diesl, Nil clean rings, J. Algebra, 383 (2013), pp. 197-211.
[13] W. B. V. Kandasamy and F. Smarandache, Some Neutrosophic Algebraic Structures and Neutrosophic n-Algebraic Structures (Arizona: Hexis Phoenix), 2006.
[14] W. B. V. Kandasamy and F. Smarandache, Neutrosophic Rings (Arizona: Hexis Phoenix), 2006.
[15] W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229 (1977), pp. 269- 278.
[16] W.K. Nicholson, Y. Zhou, Rings in which elements are uniquely the sum of an idempotent and a unit, Glasg. Math. J., 46 (2004), pp. 227-236.
[17] M. Samiei, Commutative rings whose proper homomorphic images are nil clean, Novi Sad J. Math. Vol. 50, No. 1, 2020, 37-44
[18] F. Smarandache and M. Abobala, n-Refined neutrosophic Rings, International Journal of Neutrosophic Science, vol. 5, pp. 83-90, 2020.
