On Nil-clean Neutrosophic Rings

P.

doi:https://doi.org/10.54216/GJMSA.090105

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Volume 9 • Issue 1 • PP: 45-51 • 2023

On Nil-clean Neutrosophic Rings

P. Prabakaran ^1*

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¹Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam - 638401, Tamil Nadu, India.

* Corresponding Author.

DOI https://doi.org/10.54216/GJMSA.090105

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Received: June 12, 2023 Revised: September 11, 2023 Accepted: December 04, 2023

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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.

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Prabakaran, P.. "On Nil-clean Neutrosophic Rings." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 9, no. Issue 1, 2023, pp. 45-51. DOI: https://doi.org/10.54216/GJMSA.090105

Prabakaran, P. (2023). On Nil-clean Neutrosophic Rings. Galoitica: Journal of Mathematical Structures and Applications, Volume 9(Issue 1), 45-51. DOI: https://doi.org/10.54216/GJMSA.090105

Prabakaran, P.. "On Nil-clean Neutrosophic Rings." Galoitica: Journal of Mathematical Structures and Applications Volume 9, no. Issue 1 (2023): 45-51. DOI: https://doi.org/10.54216/GJMSA.090105

Prabakaran, P. (2023) 'On Nil-clean Neutrosophic Rings', Galoitica: Journal of Mathematical Structures and Applications, Volume 9(Issue 1), pp. 45-51. DOI: https://doi.org/10.54216/GJMSA.090105

Prabakaran P. On Nil-clean Neutrosophic Rings. Galoitica: Journal of Mathematical Structures and Applications. 2023;Volume 9(Issue 1):45-51. DOI: https://doi.org/10.54216/GJMSA.090105

P. Prabakaran, "On Nil-clean Neutrosophic Rings," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 9, no. Issue 1, pp. 45-51, 2023. DOI: https://doi.org/10.54216/GJMSA.090105

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