439 232
Full Length Article
Volume 2 , Issue 2, PP: 89-94 , 2020

Title

Refined Neutrosophic Rings II

Authors Names :   E.O. Adeleke   1 *     A.A.A. Agboola   2     F. Smarandache   3  

1  Affiliation :  Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria

    Email :  yemi376@yahoo.com


2  Affiliation :  Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria

    Email :  agboolaaaa@funaab.edu.ng


3  Affiliation :  Department of Mathematics & Science, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA

    Email :  smarand@unm.edu



Doi   :  10.5281/zenodo.3728235


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 :

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[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.

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[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