Galoitica: Journal of Mathematical Structures and Applications

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Galoitica: Journal of Mathematical Structures and Applications

Volume 1 , Issue 1 , PP: 36-41, 2022 | Cite this article as | XML | Html | PDF

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

  • 1 Imam Kadhum College, Iraq - (basheerabdalrida66n@gmail.com)
  • 2 Islamic University Of Gaza, Palestine - (katyon765@gmail.com)
  • 3 Cairo University, Egypt - (rozyyy123n@gmail.com)
  • Doi: https://doi.org/10.54216/GJMSA.010103

    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 As :
    A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. "Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers." Full Length Article, Vol. 1, No. 1, 2022 ,PP. 36-41 (Doi   :  https://doi.org/10.54216/GJMSA.010103)
    A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. (2022). Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers. Journal of , 1 ( 1 ), 36-41 (Doi   :  https://doi.org/10.54216/GJMSA.010103)
    A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. "Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers." Journal of , 1 no. 1 (2022): 36-41 (Doi   :  https://doi.org/10.54216/GJMSA.010103)
    A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. (2022). Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers. Journal of , 1 ( 1 ), 36-41 (Doi   :  https://doi.org/10.54216/GJMSA.010103)
    A. Alrida Basheer , Katy D. Ahmad, Rozina Ali. Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers. Journal of , (2022); 1 ( 1 ): 36-41 (Doi   :  https://doi.org/10.54216/GJMSA.010103)
    A. Alrida Basheer, Katy D. Ahmad, Rozina Ali, Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers, Journal of , Vol. 1 , No. 1 , (2022) : 36-41 (Doi   :  https://doi.org/10.54216/GJMSA.010103)