1
Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam - 638401, Tamil Nadu, India.
(prabakaranpvkr@gmail.com)
Abstract :
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).
Keywords :
Clean ring; nil-clean ring; neutrosophic ring; refined neutrosophic ring; clean neutrosophic ring; nil-clean neutrosophic ring.
References :
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| Style | # |
|---|---|
| MLA | P. Prabakaran. "On Nil-clean Neutrosophic Rings." Galoitica: Journal of Mathematical Structures and Applications, Vol. 9, No. 1, 2023 ,PP. 45-51 (Doi : https://doi.org/10.54216/GJMSA.090105) |
| APA | P. Prabakaran. (2023). On Nil-clean Neutrosophic Rings. Journal of Galoitica: Journal of Mathematical Structures and Applications, 9 ( 1 ), 45-51 (Doi : https://doi.org/10.54216/GJMSA.090105) |
| Chicago | P. Prabakaran. "On Nil-clean Neutrosophic Rings." Journal of Galoitica: Journal of Mathematical Structures and Applications, 9 no. 1 (2023): 45-51 (Doi : https://doi.org/10.54216/GJMSA.090105) |
| Harvard | P. Prabakaran. (2023). On Nil-clean Neutrosophic Rings. Journal of Galoitica: Journal of Mathematical Structures and Applications, 9 ( 1 ), 45-51 (Doi : https://doi.org/10.54216/GJMSA.090105) |
| Vancouver | P. Prabakaran. On Nil-clean Neutrosophic Rings. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2023); 9 ( 1 ): 45-51 (Doi : https://doi.org/10.54216/GJMSA.090105) |
| IEEE | P. Prabakaran, On Nil-clean Neutrosophic Rings, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 9 , No. 1 , (2023) : 45-51 (Doi : https://doi.org/10.54216/GJMSA.090105) |