Volume 0 - 2019 , Issue II- Vol 0 , PP: 83-89, 2019 | Cite this article as | XML | Html | PDF | Full Length Article
Binu R 1 *
Doi: https://doi.org/10.54216/IJNS.000204
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.
Neutrosophic algebra over a neutrosophic subfield, Neutrosophic ideal, Neutrosophic quotient algebra.
[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.