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Galoitica: Journal of Mathematical Structures and Applications

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Online: 2834-5568
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Galoitica: Journal of Mathematical Structures and Applications
Full Length Article

Volume 1Issue 1PP: 36-41 • 2022

Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers

A. Alrida Basheer 1* ,
Katy D. Ahmad 2 ,
Rozina Ali 3
1Imam Kadhum College, Iraq
2Islamic University Of Gaza, Palestine
3Cairo University, Egypt
* Corresponding Author.
Received: February 05, 2022 Accepted: April 08, 2022

Abstract

The objective of this paper is to present a new class of Diophantine equations derived from the group of units problem of n-cyclic refined neutrosophic rings of integers by using homomorphisms between these rings and a finite Cartesian product ring of Z with itself.

Also, this work provides many examples about this class and its solvability as a new application of neutrosophic algebraic structures in number theory.

Keywords

n-cyclic refined neutrosophic ring n-cyclic refined neutrosophic integer group of units

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Cite This Article

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Basheer, A. Alrida, Ahmad, Katy D., Ali, Rozina. "Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 1, no. Issue 1, 2022, pp. 36-41. DOI: https://doi.org/10.54216/GJMSA.010103
Basheer, A., Ahmad, K., Ali, R. (2022). Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers. Galoitica: Journal of Mathematical Structures and Applications, Volume 1(Issue 1), 36-41. DOI: https://doi.org/10.54216/GJMSA.010103
Basheer, A. Alrida, Ahmad, Katy D., Ali, Rozina. "Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers." Galoitica: Journal of Mathematical Structures and Applications Volume 1, no. Issue 1 (2022): 36-41. DOI: https://doi.org/10.54216/GJMSA.010103
Basheer, A., Ahmad, K., Ali, R. (2022) 'Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers', Galoitica: Journal of Mathematical Structures and Applications, Volume 1(Issue 1), pp. 36-41. DOI: https://doi.org/10.54216/GJMSA.010103
Basheer A, Ahmad K, Ali R. Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers. Galoitica: Journal of Mathematical Structures and Applications. 2022;Volume 1(Issue 1):36-41. DOI: https://doi.org/10.54216/GJMSA.010103
A. Basheer, K. Ahmad, R. Ali, "Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 1, no. Issue 1, pp. 36-41, 2022. DOI: https://doi.org/10.54216/GJMSA.010103
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