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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 2 , Issue 2 , PP: 89-94, 2020 | Cite this article as | XML | Html | PDF | Full Length Article

Refined Neutrosophic Rings II

E.O. Adeleke 1 * , A.A.A. Agboola 2 , F. Smarandache 3

  • 1 Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria - (yemi376@yahoo.com)
  • 2 Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria - (agboolaaaa@funaab.edu.ng)
  • 3 Department of Mathematics & Science, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA - (smarand@unm.edu)

    • Doi: https://doi.org/10.54216/IJNS.020205

    Abstract

    This paper is the continuation of the work started in the paper titled “Refined Neutrosophic Rings I”. In the present paper, we study refined neutrosophic ideals and refined neutrosophic homomorphisms along their elementary properties. It is shown that if R = Z(I1, I2) is a refined neutrosophic ring of integers and J = nZ(I1, I2) is a refined neutrosophic ideal of R, then R/J Zn(I1, I2).

    Keywords :

    Neutrosophy, refined neutrosophic ring, refined neutrosophic ideal, refined neutrosophic ring homomorphism

    References

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

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

    [3] Agboola, A.A.A.; Davvaz, B. “On Neutrosophic Canonical Hypergroups and Neutrosophic Hyperrings”, Neutrosophic Sets and Systems, vol 2, pp. 34-41, 2014.

    [4] Agboola, A.A.A.; Adeleke, E.O.; Akinleye, S.A. “Neutrosophic Rings II”, Int. J. of Math. Comb., vol 2, pp. 1-8, 2012.

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

    [6] Agboola,A.A.A,; Davvaz,B.; Smarandache,F. “Neutrosophic Quadruple Hyperstructures”, Annals of Fuzzy Mathematics and Informatics, vol 14 (1), pp. 29-42, 2017.

    [7] Akinleye,S.A.; Adeleke,E.O. ; Agboola,A.A.A. “Introduction to Neutrosophic Nearrings”, Annals of Fuzzy Mathematics and Informatics, vol 12 (3), pp. 397-410, 2016.

    [8] Akinleye, S.A.; Smarandache,F.; Agboola,A.A.A. “On Neutrosophic Quadruple Algebraic Structures”, Neutrosophic Sets and Systems, vol 12, pp. 122-126, 2016.

    [9] Adeleke,E.O; Agboola, A.A.A ; Smarandache, F. “Refined Neutrosophic Rings I”, (Submitted for publi-cation in Neutrosophic Sets and Systems).

    [10] Smarandache,F. “ A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability”, (3rd edition), American Research Press, Rehoboth,(2003),

    http://fs.gallup.unm.edu/eBook-Neutrosophic4.pdf.

    [11] Smarandache,F. “n-Valued Refined Neutrosophic Logic and Its Applications in Physics”, Progress in Physics, USA, vol 4 (2013), pp. 143-146, 2013.

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

    3- 10, 2015.

    [13] Vasantha Kandasamy,W.B; Smarandache,F. “ Neutrosophic Rings”, Hexis, Phoenix, Arizona,(2006), http://fs.gallup.unm.edu/NeutrosophicRings.pdf

    Cite This Article As :
    Adeleke, E.O.. , Agboola, A.A.A.. , Smarandache, F.. Refined Neutrosophic Rings II. International Journal of Neutrosophic Science, vol. , no. , 2020, pp. 89-94. DOI: https://doi.org/10.54216/IJNS.020205
    Adeleke, E. Agboola, A. Smarandache, F. (2020). Refined Neutrosophic Rings II. International Journal of Neutrosophic Science, (), 89-94. DOI: https://doi.org/10.54216/IJNS.020205
    Adeleke, E.O.. Agboola, A.A.A.. Smarandache, F.. Refined Neutrosophic Rings II. International Journal of Neutrosophic Science , no. (2020): 89-94. DOI: https://doi.org/10.54216/IJNS.020205
    Adeleke, E. , Agboola, A. , Smarandache, F. (2020) . Refined Neutrosophic Rings II. International Journal of Neutrosophic Science , () , 89-94 . DOI: https://doi.org/10.54216/IJNS.020205
    Adeleke E. , Agboola A. , Smarandache F. [2020]. Refined Neutrosophic Rings II. International Journal of Neutrosophic Science. (): 89-94. DOI: https://doi.org/10.54216/IJNS.020205
    Adeleke, E. Agboola, A. Smarandache, F. "Refined Neutrosophic Rings II," International Journal of Neutrosophic Science, vol. , no. , pp. 89-94, 2020. DOI: https://doi.org/10.54216/IJNS.020205

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