Volume 8 • Issue 2 • PP: 38-48 • 2024
On The 4-Cyclic Refined Neutrosophic Solutions of The Diophantine Equation X^n=1 and m-Cyclic Refined Neutrosophic Modulo Integers
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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The ring of n-cyclic refined neutrosophic integers is a logical extension of the integer ring Z based on a special multiplication operation defined between the indeterminacy algebraic elements. In this paper, we provide a full description of the 4-cyclic refined neutrosophic integer roots of unity, where we prove that for odd values of n we get exactly two different solutions. For even values of n, we get exactly 15 different solutions. On the other hand, we characterize the m-cyclic refined neutrosophic modulo integers rings and present many of their algebraic properties based on neutrosophic homomorphisms and substructures.
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References
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