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Title

Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers

  Oliver Von Shtawzen 1 *

1  University Of Nizwa, Nizwa, Sultanate Of Oman
    (Vonshtawzen1970abc@gmail.com)

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Doi   :   https://doi.org/10.54216/JNFS.030203

Received: April 02, 2022 Accepted: July 12, 2022

Abstract :

The objective of this paper is to suggest two new conjectures concerning the invertible elements in 3-cyclic, and 4-cyclic refined neutrosophic rings of integers, where the invertibility condition shows that the solution of some Diophantine equations may determine the classification of the group of units of these algebraic rings.

Keywords :

n-cyclic refined neutrosophic ring , n-cyclic refined integer , group of units , Turiyam rings

References :

[1] A. G. Agarg¨um, D. D. Anderson, and S. Valdes-Leon, “Factorization in commutative rings with zero divisors III”, Rocky Mountain J. Math. 31 (2001), 1–21.

[2] D. D. Anderson, and R. Markanda, “Unique factorization rings with zero divisors”, Houston J. Math. 11 (1985), 15–30.

[3] Abobala, M, "n-Cyclic Refined Neutrosophic Algebraic Systems Of Sub-Indeterminacies, An Application To Rings and Modules", International Journal of Neutrosophic Science, Vol. 12, pp. 81-95 . 2020.

[4] Sadiq. B., " A Contribution To The group Of Units Problem In Some 2-Cyclic Refined neutrosophic Rings ", International Journal Of Neutrosophic Science, 2022.

[5] Smarandache, F., " A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability", American Research Press. Rehoboth, 2003.

[6] Adeleke, E.O., Agboola, A.A.A., and Smarandache, F.,  "Refined Neutrosophic Rings I", International Journal of Neutrosophic Science, Vol. 2(2), pp. 77-81. 2020.

[7] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", Neutrosophic Sets and Systems, Vol. 45, 2021.

[8] Olgun, N., Hatip, A., Bal, M., and Abobala, M., " A Novel Approach To Necessary and Sufficient Conditions For The Diagonalization of Refined Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 16, pp. 72-79, 2021.

[9] Abobala, M., Bal, M., and Hatip, A.," A Review On Recent Advantages In Algebraic Theory Of Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 17, 2021.

[10] Abobala, M., Bal, M., and Aswad, M., "A Short Note On Some Novel Applications of Semi Module Homomorphisms", International journal of neutrosophic science, 2022.

[11] P. Ribenboim, “Rings of generalized power series. II. Units and zero-divisors”, J. Algebra 168 (1994), 71–89.

[12] Z. Pogorzaly, “A generalization of trivial extension algebras”, J. Pure Appl. Algebra 203 (2005), 145–165.

[13] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 45, 2021.

[14] E. Adeleke. A. Agboola., and F. Smarandache. “Refined Neutrosophic Rings II”. International Journal of Neutrosophic Science, Vol. 2, 2020. pp. 89-94.

[15] D. G. Northcott, “Lessons on Rings, Modules, and Multiplicities”, Cambridge Univ. Press, Cambridge, 1968.

[16] Singh, P. K., Ahmad, K., Bal, M., and Aswad, M., " On The Symbolic Turiyam rings", Journal of Neutrosophic and Fuzzy Systems, Vol. 1, Issue 2, pp. 80-88, 2022.

 [17] Bal M., Singh P. K., and Ahmad K. D., “ An Introduction To The Symbolic Turiyam R-Modules and Turiyam Modulo Integers”, Journal of Neutrosophic and Fuzzy Systems, Vol. 2 , No. 2 , (2022) : 8-19

[18] Bal M., Singh P. K., and Ahmad K. D., “A Short Introduction To The Concept Of Symbolic Turiyam Matrix”, Journal of Neutrosophic and Fuzzy Systems, Vol. 2 , No. 1 , (2022) : 88-99

[19] Singh, P,K., " Data With Turiyam Set for Fourth Dimension Quantum Information Processing", Journal of Neutrosophic and Fuzzy Systems, Vol.1, 2022.

[20] Singh P. K., “A Note on Basic Proof of Some Famous Mathematical Theorem and Its Illustration”, Journal of Neutrosophic and Fuzzy Systems, Vol. 3 , No. 1 , (2022) : 39-53 

Cite this Article as :
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MLA Oliver Von Shtawzen. "Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers." Full Length Article, Vol. 3, No. 2, 2022 ,PP. 32-36 (Doi   :  https://doi.org/10.54216/JNFS.030203)
APA Oliver Von Shtawzen. (2022). Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers. Journal of Full Length Article, 3 ( 2 ), 32-36 (Doi   :  https://doi.org/10.54216/JNFS.030203)
Chicago Oliver Von Shtawzen. "Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers." Journal of Full Length Article, 3 no. 2 (2022): 32-36 (Doi   :  https://doi.org/10.54216/JNFS.030203)
Harvard Oliver Von Shtawzen. (2022). Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers. Journal of Full Length Article, 3 ( 2 ), 32-36 (Doi   :  https://doi.org/10.54216/JNFS.030203)
Vancouver Oliver Von Shtawzen. Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers. Journal of Full Length Article, (2022); 3 ( 2 ): 32-36 (Doi   :  https://doi.org/10.54216/JNFS.030203)
IEEE Oliver Von Shtawzen, Conjectures for Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers, Journal of Full Length Article, Vol. 3 , No. 2 , (2022) : 32-36 (Doi   :  https://doi.org/10.54216/JNFS.030203)
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