International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 7 , Issue 2 , PP: 87-96, 2020 | Cite this article as | XML | Html | PDF | Full Length Article

On Refined Neutrosophic R-module

Necati Olgun 1 * , Ahmed Hatip 2

  • 1 Department of Mathematics, Gaziantep University, Turkey - (olgun@gantep.edu.tr)
  • 2 Department of Mathematics, Gaziantep University, Turkey - (kollnaar5@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.070201

    Abstract

    Modules are one of the fundamental and rich algebraic structure concerning some binary operations in the study of algebra. In this paper, some basic structures of refined neutrosophic R-modules and refined neutrosophic submodules in algebra are generalized. Some properties of refined neutrosophic R-modules and refined neutrosophic submodules are presented. More precisely, classical modules and refined neutrosophic rings are utilized. Consequently, refinedneutrosophic R- modules that are completely different from the classical modular in the structural properties are introduced. Also, neutrosophic R-module homomorphism is explained and some definitions and theorems are presented.  

    Keywords :

    Refined  , neutrosophic group,  , refined  , neutrosophic ring,  , refined  , neutrosophic R-module, weak  , refined  , neutrosophic R-module, strong  , refined  , neutrosophic R-module,  , refined  , neutrosophic R-module homomorphism.

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    References

    [1] A. A. A. Agboola, On Refined Neutrosophic Algebraic StructuresNeutrosophic Sets and Systems, vol.10, pp. 99-101, 2015. 

    [2] A. A. A. Agboola, A. D. Akinola and O.Y.Oyebola, Neutrosophic Rings IInt. J. of Math. Comb., vol. 4, pp. 1-14, 2011. 

    [3] A. A. A. Agboola, E. O. Adeleke and S. A. Akinleye, Neutrosophic Rings IIInt. J. of Math. Comb., vol.2, pp. 1-8, 2012.

    [4] A. A. A. Agboola, Akwu A. O. and Y. T. Oyebo, Neutrosophic Groups and Neutrosopic Subgroups, Int. J. of Math. Comb., vol. 3, pp. 1-9, 2012. 

    [5] E. O. Adeleke, A. A. A. Agboola and F. Smarandache, Refined Neutrosophic Rings IInternational Journal of Neutrosophic Science , vol. 2, pp. 77-81, 2020. 

    [6] E. O. Adeleke, A. A. A. Agboola and F. Smarandache, Refined Neutrosophic Rings IIInternational Journal of Neutrosophic Science, vol. 2, pp. 89-94, 2020. 

    [7] F. Smarandache, n-Valued Refined Neutrosophic Logic and Its Applications in PhysicsProgress in Physics, USA, vol. 4, pp. 143-146, 2013.

    [8] F. Smarandache,  (T,I,F)-Neutrosophic Structures, Neutrosophic Sets and Systems,vol.8, pp.3-10, 2015. 

    [9] A.A.A. Agboola and S. A. Akinleye, “Neutrosophic Vector Space”, Neutrosophic Sets and Systems, Vol. 4, pp. 9-18, 2014.

    [10] W. B. Vasantha Kandasamy and F. Smarandache, “Neutrosophic Rings”, Hexis, Phoenix, Arizona, 2006 http://fs.unm.edu/NeutrosophicRings.pdf

    [11] W. B. Vasantha Kandasamy & Florentin Smarandache, “Basic Neutrosophic Algebraic Structures and their Applications to Fuzzy and Neutrosophic Models”, Hexis, 2004.

    [12] A. B. AL-Nafee, R. K. Al-Hamido, F.Smarandache, “Separation Axioms In Neutrosophic Crisp Topological Spaces”, Neutrosophic Sets and Systems, vol. 25, pp.25-32, 2019. 

    [13] R. K. Al-Hamido, “Neutrosophic Crisp Bi-Topological Spaces”, Neutrosophic Sets and Systems, Vol. 21, pp.66-73, 2018.

    [14] M. Al-Tahan, and B. Davvaz, “Refined neutrosophic quadruple (poly-)hypergroups and their fundamental group”, Neutrosophic Sets and Systems, vol. 27, pp. 138-153, 2019.

    [15] A. Chakraborty, S. Broumi, P. K Singh; “Some properties of Pentagonal Neutrosophic Numbers and its Applications in Transportation Problem EnvironmentNeutrosophic Sets and Systems, vol.28, pp.200-215, 2019. 

    [16] S. Broumi, M. Talea, A. Bakali,  F. Smarandache, Single Valued Neutrosophic GraphsJournal of  New Theory, N 10,  pp. 86-101, 2016. 

    [17] Nguyen Tho Thong, Luu Quoc Datc, Le Hoang Son, Nguyen Dinh Hoa, Mumtaz Alid, Florentin Smarandache, "Dynamic interval valued neutrosophic set: Modeling decision making in dynamic environments," Computers in Industry, vol. 108, pp. 45-52, 2019. 

    [18] S.Broumi, M. Talea, A. Bakali, P. K.Singh, F. Smarandache,”Energy and Spectrum Analysis of Interval Valued Neutrosophic Graph using MATLAB”, Neutrosophic Sets and Systems, vol. 24, pp. 46-60, 2019.

    [19] A. Hatip, "The Special Neutrosophic Functions," International Journal of Neutrosophic Science , Vol. 4, no. 2, pp. 104-116, 15 April 2020.

    [20]S. Broumi, M. Talea, A.Bakali,  F. Smarandache, “On Bipolar Single Valued Neutrosophic Graphs”,  Journal of  New Theory, N11, pp.84-102, 2016.

    [21] S. Broumi, M. Talea, A. Bakali, F. Smarandache, Interval Valued Neutrosophic GraphsSISOM & ACOUSTICS, Bucharest , Volume X, pp.79-91, 2016. 

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

    [23] S. Broumi, M. Talea, F. Smarandache and A. Bakali, Single Valued Neutrosophic Graphs:  Degree, Order and Size”, IEEE International Conference on Fuzzy Systems (FUZZ), pp.2444-2451, 2016.

    [24] Mohamed Bisher Zeina, Neutrosophic Event-Based Queueing ModelInternational Journal of Neutrosophic Science, Vol. 6, No. 1, pp. 48-55, 2020.

    [25] Mohamed Bisher Zeina, Erlang Service Queueing Model with Neutrosophic ParametersInternational Journal of Neutrosophic Science, Vol. 6, No. 2, pp.106-112, 2020.

    Cite This Article As :
    Olgun, Necati. , Hatip, Ahmed. On Refined Neutrosophic R-module. International Journal of Neutrosophic Science, vol. , no. , 2020, pp. 87-96. DOI: https://doi.org/10.54216/IJNS.070201
    Olgun, N. Hatip, A. (2020). On Refined Neutrosophic R-module. International Journal of Neutrosophic Science, (), 87-96. DOI: https://doi.org/10.54216/IJNS.070201
    Olgun, Necati. Hatip, Ahmed. On Refined Neutrosophic R-module. International Journal of Neutrosophic Science , no. (2020): 87-96. DOI: https://doi.org/10.54216/IJNS.070201
    Olgun, N. , Hatip, A. (2020) . On Refined Neutrosophic R-module. International Journal of Neutrosophic Science , () , 87-96 . DOI: https://doi.org/10.54216/IJNS.070201
    Olgun N. , Hatip A. [2020]. On Refined Neutrosophic R-module. International Journal of Neutrosophic Science. (): 87-96. DOI: https://doi.org/10.54216/IJNS.070201
    Olgun, N. Hatip, A. "On Refined Neutrosophic R-module," International Journal of Neutrosophic Science, vol. , no. , pp. 87-96, 2020. DOI: https://doi.org/10.54216/IJNS.070201