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International Journal of Neutrosophic Science
Volume 0 - 2019 , Issue II- Vol 0, PP: 83-89 , 2019 | Cite this article as | XML | Html |PDF

Title

Neutrosophic Quotient Algebra

  Binu R 1 *

1  Rajagiri School of Engineering and Technology, Kerala, India
    (1984binur@gmail.com)


Doi   :   https://doi.org/10.54216/IJNS.000204

Received: February 11, 2019 Revised: April 20, 2019 Accepted: April 29, 2019

Abstract :

The algebraic properties of neutrosphic ideals over algebra, isomorphism properties of neutrosophic ideal and neutrosophic modules over algebra are discussed in this paper. Some of the charactrisations of Neutrosophic quotient algebra are derived and the role of algebraic structures is studied in the context of neutrosophic set.  This paper expands the definition of quotient algebra within the context of neutrosophical set.

Keywords :

Neutrosophic algebra over a neutrosophic subfield , Neutrosophic ideal , Neutrosophic quotient algebra.

References :

[1]    Zadeh, Lotfi A. "Fuzzy sets." Information and control 8.3, 338-353, 1965.

[2]    Atanassov, Krassimir. "Intuitionistic fuzzy sets." International Journal Bioautomation 20, 2016.

[3]    F. Smarandache. Neutrosophy / Neutrosophic probability, set, and logic, American Research Press, 1998. See also: http://gallup.unm.edu/~smarandache/NeutLog.txt.

[4]    Smarandache, Florentin. "Neutrosophic set-a generalization of the intuitionistic fuzzy set." International journal of pure and applied mathematics 24.3, 287, 2005.

[5]    Smarandache, Florentin, ed. A unifying field in logics: Neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability: Neutrosophic logic: neutrosophy, neutrosophic set, neutrosophic probability. Infinite Study, 2003.

[6]    Wang, Haibin, et al. Single valued neutrosophic sets. Infinite study, 2010.

[7]    Kandasamy, WB Vasantha, and Florentin Smarandache. Basic neutrosophic algebraic structures and their application to fuzzy and neutrosophic models. Vol. 4. Infinite Study, 2004.

[8]    Robinson, Abraham. Non-standard analysis. Princeton University Press, 2016.

[9]    Smarandache, Florentin, ed. A unifying field in logics: Neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability: Neutrosophic logic: neutrosophy, neutrosophic set, neutrosophic probability. Infinite Study, 2003.

[10] Smarandache, Florentin. "Neutrosophic set–a generalization of the intuitionistic fuzzy set." Journal of Defense Resources Management (JoDRM) 1.1,pp.107-116, 2010.

[11] Hazewinkel, Michiel; Gubareni, Nadiya; Kirichenko, Vladimir V. (2004). Algebras, rings and modules. 1. Springer. ISBN 1-4020-2690-0.

[12] Kunz, Ernst. Introduction to commutative algebra and algebraic geometry. Springer Science & Business Media, 2012.

[13] Broumi S., Son L.H., Bakali A., Talea M., Smarandache F., Selvachandran G., “Computing Operational Matrices in Neutrosophic Environments: A Matlab Toolbox”,  Neutrosophic Sets and Systems, Vol. 18, pp.58-66, 2017.

[14] Broumi S., Bakali A., Talea M,, and Smarandache F,”Isolated Single Valued Neutrosophic Graphs”, Neutrosophic Sets and Systems, Vol. 11, pp.74-78, 2016.

[15] Broumi S., Dey A., Bakali A., Talea M., Smarandache F., Son L. H., Koley D., “Uniform Single Valued Neutrosophic Graphs”, Neutrosophic Sets and Systems, Vol. 17, pp.42-49, 2017.

 

 


Cite this Article as :
Style #
MLA Binu R. "Neutrosophic Quotient Algebra." International Journal of Neutrosophic Science, Vol. 0 - 2019, No. II- Vol 0, 2019 ,PP. 83-89 (Doi   :  https://doi.org/10.54216/IJNS.000204)
APA Binu R. (2019). Neutrosophic Quotient Algebra. Journal of International Journal of Neutrosophic Science, 0 - 2019 ( II- Vol 0 ), 83-89 (Doi   :  https://doi.org/10.54216/IJNS.000204)
Chicago Binu R. "Neutrosophic Quotient Algebra." Journal of International Journal of Neutrosophic Science, 0 - 2019 no. II- Vol 0 (2019): 83-89 (Doi   :  https://doi.org/10.54216/IJNS.000204)
Harvard Binu R. (2019). Neutrosophic Quotient Algebra. Journal of International Journal of Neutrosophic Science, 0 - 2019 ( II- Vol 0 ), 83-89 (Doi   :  https://doi.org/10.54216/IJNS.000204)
Vancouver Binu R. Neutrosophic Quotient Algebra. Journal of International Journal of Neutrosophic Science, (2019); 0 - 2019 ( II- Vol 0 ): 83-89 (Doi   :  https://doi.org/10.54216/IJNS.000204)
IEEE Binu R, Neutrosophic Quotient Algebra, Journal of International Journal of Neutrosophic Science, Vol. 0 - 2019 , No. II- Vol 0 , (2019) : 83-89 (Doi   :  https://doi.org/10.54216/IJNS.000204)