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Title

A Short Contribution To Von Shtawzen's Abelian Group In n-Cyclic Refined Neutrosophic Rings

  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/JNFS.030206

Received: April 06, 2022 Accepted: July 17, 2022

Abstract :

This paper is dedicated to study the group of units (Von Shtawzen's group) of some numerical n-cyclic refined neutrosophic rings such as integer, rational, and real case. Where we write the elements of these abelian groups by using equations derived from the values of some circulant numerical  determinants.

Keywords :

n-cyclic refined neutrosophic ring , n-cyclic refined integer , group of units , Von Shtawzen's abelian group.

References :

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

[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., 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] Von Shtawzen, O., " Conjectures For Invertible Diophantine Equations Of 3-Cyclic and 4-Cyclic Refined Integers", Journal Of Neutrosophic And Fuzzy Systems, Vol. 3 , No. 2 , pp. 32-36, 2022.

[17] Abobala, M., Hatip, A., Bal,M.," A Study Of Some Neutrosophic Clean Rings", International journal of neutrosophic science, 2022

[18] Smarandache, F., and Abobala, M., n-Refined neutrosophic Rings, International Journal of Neutrosophic Science, Vol. 5 , pp. 83-90, 2020.

[19] Abobala, M.,. "A Study of AH-Substructures in n-Refined Neutrosophic Vector Spaces", International Journal of Neutrosophic Science", Vol. 9, pp.74-85. 2020.

[20] Sankari, H., and Abobala, M." n-Refined Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 36, pp. 1-11. 2020.

[21] Abobala, M., " n-Refined Neutrosophic Groups I", International Journal of Neutrosophic Science, Vol. 0, pp. 27-34. 2020.

[22] Abobala, M., "Classical Homomorphisms Between n-refined Neutrosophic Rings", International Journal of Neutrosophic Science", Vol. 7, pp. 74-78. 2020.

[23] Abobala, M., A Study of Maximal and Minimal Ideals of n-Refined Neutrosophic Rings, Journal of Fuzzy Extension and Applications, Vol. 2, pp. 16-22, 2021.

[24] Smarandache F., and Abobala, M.,  "n-Refined Neutrosophic Vector Spaces", International Journal of Neutrosophic Science, Vol. 7, pp. 47-54. 2020.

[25] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021

[26] Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic Equations, Journal Of Mathematics, Hindawi, 2021

[27] Abobala, M., " Semi Homomorphisms and Algebraic Relations Between Strong Refined Neutrosophic Modules and Strong Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 39, 2021

[28] Abobala, M., "On Some Special Substructures of Refined Neutrosophic Rings", International Journal of Neutrosophic Science, Vol. 5, pp. 59-66. 2020.

[29] Singh P. K., “Three-way n-valued neutrosophic concept lattice at different granulation”, International Journal of Machine Learning and Cybernetics, Vol 9, Issue 11, pp. 1839-1855, 2018.

[30] Singh P. K., “AntiGeometry and NeutroGeometry Characterization of Non-Euclidean Data Sets”, Journal of Neutrosophic and Fuzzy Systems, Vol 1, Issue 1, pp. 24-33, 2021,  DOI: https://doi.org/10.54216/JNFS.0101012

[31] Singh, P,K., “Data with Non-Euclidean Geometry and its Characterization”, Journal of Artificial Intelligence and Technology, Vol 2, Issue 1, pp. 3-8, 2022.

[32] Singh P. K. “NeutroAlgebra and NeutroGeometry for Dealing Heteroclinic Patterns”. In: Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras, IGI Global Publishers, April 2022, Chapter 6,  DOI: 10.4018/978-1-6684-3495-6, ISBN13: 9781668434956

[33] Singh P. K. “Non-Euclidean, Anti-Geometry and NeutroGeometry Characterization”, International Journal of Neutrosophic Sciences, Vol 18, Issue 3, pp. 8-19, 2022.

 


Cite this Article as :
Style #
MLA A .Alrida Basheer , Katy D. Ahmad, Rozina Ali. "A Short Contribution To Von Shtawzen's Abelian Group In n-Cyclic Refined Neutrosophic Rings." Full Length Article, Vol. 3, No. 2, 2022 ,PP. 53-56 (Doi   :  https://doi.org/10.54216/JNFS.030206)
APA A .Alrida Basheer , Katy D. Ahmad, Rozina Ali. (2022). A Short Contribution To Von Shtawzen's Abelian Group In n-Cyclic Refined Neutrosophic Rings. Journal of Full Length Article, 3 ( 2 ), 53-56 (Doi   :  https://doi.org/10.54216/JNFS.030206)
Chicago A .Alrida Basheer , Katy D. Ahmad, Rozina Ali. "A Short Contribution To Von Shtawzen's Abelian Group In n-Cyclic Refined Neutrosophic Rings." Journal of Full Length Article, 3 no. 2 (2022): 53-56 (Doi   :  https://doi.org/10.54216/JNFS.030206)
Harvard A .Alrida Basheer , Katy D. Ahmad, Rozina Ali. (2022). A Short Contribution To Von Shtawzen's Abelian Group In n-Cyclic Refined Neutrosophic Rings. Journal of Full Length Article, 3 ( 2 ), 53-56 (Doi   :  https://doi.org/10.54216/JNFS.030206)
Vancouver A .Alrida Basheer , Katy D. Ahmad, Rozina Ali. A Short Contribution To Von Shtawzen's Abelian Group In n-Cyclic Refined Neutrosophic Rings. Journal of Full Length Article, (2022); 3 ( 2 ): 53-56 (Doi   :  https://doi.org/10.54216/JNFS.030206)
IEEE A .Alrida Basheer, Katy D. Ahmad, Rozina Ali, A Short Contribution To Von Shtawzen's Abelian Group In n-Cyclic Refined Neutrosophic Rings, Journal of Full Length Article, Vol. 3 , No. 2 , (2022) : 53-56 (Doi   :  https://doi.org/10.54216/JNFS.030206)