425 221
Full Length Article
Volume 7 , Issue 2, PP: 87-96 , 2020


On Refined Neutrosophic R-module

Authors Names :   Necati Olgun   1 *     Ahmed Hatip   2  

1  Affiliation :  Department of Mathematics, Gaziantep University, Turkey

    Email :  olgun@gantep.edu.tr

2  Affiliation :  Department of Mathematics, Gaziantep University, Turkey

    Email :  kollnaar5@gmail.com

Doi   :  10.5281/zenodo.3881963

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.


References :

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

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

[3] A. A. A. Agboola, E. O. Adeleke and S. A. Akinleye, “Neutrosophic Rings II”, Int. 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 I”, International Journal of Neutrosophic Science , vol. 2, pp. 77-81, 2020. 

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

[7] F. Smarandache, “n-Valued Refined Neutrosophic Logic and Its Applications in Physics”, Progress 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 Environment”, Neutrosophic Sets and Systems, vol.28, pp.200-215, 2019. 

[16] S. Broumi, M. Talea, A. Bakali,  F. Smarandache, “Single Valued Neutrosophic Graphs”, Journal 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 Graphs”, SISOM & 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 Model”, International Journal of Neutrosophic Science, Vol. 6, No. 1, pp. 48-55, 2020.

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