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International Journal of Neutrosophic Science

ISSN
Online: 2690-6805 Print: 2692-6148
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Continuous publication

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Open access · Articles freely available online · APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Volume 2Issue 2PP: 89-94 • 2020

Refined Neutrosophic Rings II

E.O. Adeleke 1* ,
A.A.A. Agboola 1 ,
F. Smarandache 2
1Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria
2Department of Mathematics & Science, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA
* Corresponding Author.

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

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Adeleke, E.O., Agboola, A.A.A., Smarandache, F.. "Refined Neutrosophic Rings II." International Journal of Neutrosophic Science, vol. Volume 2, no. Issue 2, 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, Volume 2(Issue 2), 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 Volume 2, no. Issue 2 (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, Volume 2(Issue 2), pp. 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. 2020;Volume 2(Issue 2):89-94. DOI: https://doi.org/10.54216/IJNS.020205
E. Adeleke, A. Agboola, F. Smarandache, "Refined Neutrosophic Rings II," International Journal of Neutrosophic Science, vol. Volume 2, no. Issue 2, pp. 89-94, 2020. DOI: https://doi.org/10.54216/IJNS.020205
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