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Full Length Article
Volume 10 , Issue 1, PP: 09-22 , 2020


Introduction to Neutrosophic Hypernear-rings

Authors Names :   M.A. Ibrahim   1 *     A.A.A. Agboola   2  

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

    Email :  muritalaibrahim40@gmail.com

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

    Email :  agboolaaaa@funaab.edu.ng

Doi   :  10.5281/zenodo.4001123

Received: April 25, 2020 Accepted: August 01, 2020

Abstract :

This paper is concerned with the introduction of neutrosophic hypernear-rings. The concept of Neutrosophic A-hypergroup of a hypernear-ring A; neutrosophic A(I)-hypergroup of a neutrosophic hypernear-ring A(I) and their respective neutrosophic substructures are defined. We investigate and present some interesting results arising from the study of hypernear-rings in neutrosophic environment. It is shown that a constant Neutrosophic hypernear-ring in general is not a constant hypernear-ring. In addition, we consider the neutrosophic ideals, neutrosophic homomorphism and neutrosophic quotient hypernear-rings of neutrosophic hypernear-rings. 

Keywords :


neutrosophy , neutrosophic hypernear-ring , neutrosophic A-hypergroup , neutrosophic A(I)-hypergroup , neutrosophic A-subhypergroup , neutrosophic A(I)-subhypergroup , neutrosophic

hyperideals , neutrosophic hypernear-ring homomorphism , neutrosophic A-hypergroup homomorphism.

References :

[1]     Agboola, A.A.A. and Akinleye, S.A., jjNeutrosophic Hypervector Spacesjj, ROMAI Journal, Vol.11, pp. 1-16, 2015.

[2]     Agboola, A.A.A and Davvaz, B., jjOn Neutrosophic Canonical Hypergroups and Neutrosophic Hyperringsjj, Neutrosophic Sets and Systems. Vol.2, pp. 34-41, 2014.

[3]     Agboola, A.A.A and Davvaz, B., jjIntroduction to Neutrosophic Hypergroupsjj, ROMAI J., Vol.9(2), pp. 1-10, 2013.

[4]     Agboola,A.A.A., Davvaz, B. and Smarandache,F. jjNeutrosophic quadruple algebraic hyperstructuresjj, Ann. Fuzzy Math.Inform. Vol.14, pp. 29-42, 2017.

[5]     Agboola, A.A.A, Ibrahim, M.A., Adeleke, E.O, Akinleye, S.A., jjOn Refined Neutrosophic Algebraic Hyperstructures Ijj, International Journal of Neutrosophic Science (IJNS), Vol. 5(1), pp. 29-37, 2020.

[6]     Akinleye, S.A., Adeleke, E.O. and Agboola, A.A.A. jjIntroduction to neutrosophic near-ringsjj, Ann. Fuzzy Math.Inform. Vol.12, pp. 397-409, 2016.

[7]     Al-Tahan, M. and Davvaz, B., jj Refined neutrosophic quadruple (po-)hypergroups and their fundamental group jj, Neutrosophic Sets and Systems, Vol. 27, pp. 138-153, 2019.

[8]     Corsini. P., jjHypergroupes regulier et hypermodulesjj, Vol 20, pp. 121-135, 1975.

[9]     Corsini. P., jjProlegomena of Hypergroup Theoryjj, Aviani Editore, Tricemo, Italian, 1993.

[10]     Corsini. P. and Loereanu, V. jjApplication of Hyperstructure Theoryjj, Vol.5 Advances in Mathematics. Kluwer Academics Publishers, Dordrecht, The Netherlands, 2003.

[11]     Dasic, V., jjHypernear-rings, Algebraic Hyperstructures and Applicationsjj, Proceedings of the Fourth International Congress Xanthi, Greece, pp. 75-85, World Sci. Publ., Teaneck, NJ, 1991.

[12]     Davvaz, B. and Leoreanu-Fotea, V., jjHyperring Theory and Applicationsjj, International Academic Press,Palm Harber, USA, 2007.

[13]     Gontineac, V.M., jjOn hypernear-rings and H-hypergroupsjj, Proc. Fifth Int. Congress on Algebraic Hy- perstrutures and Application (AHA 1993), Hadronic Press, Inc., USA, pp. 171-179, 1994.

[14]     Ibrahim, M.A.,Agboola, A.A.A, Adeleke, E.O, Akinleye, S.A., jjIntroduction to Neutrosophic Subtrac- tion Algebra and Neutrosophic Subtraction Semigroupjj, International Journal of Neutrosophic Science (IJNS), Vol. 2(2), pp. 47-62, 2020.

[15]     Ibrahim, M.A.,Agboola, A.A.A, Adeleke, E.O, Akinleye, S.A., jjOn Neutrosophic Quadruple Hypervec-tor Spacesjj, International Journal of Neutrosophic Science (IJNS), Vol. 4(1), pp. 20-35, 2020.

[16]     Ibrahim, M.A.,Agboola, A.A.A, Badmus, B.S, Akinleye, S.A., jjOn Refined Neutrosophic Hypervector Spacesjj, International Journal of Neutrosophic Science (IJNS), Vol. 8(1), pp. 50-71, 2020.

[17]     Ibrahim, M.A.,Agboola, A.A.A, Badmus, B.S, Akinleye, S.A., jjOn Refined Neutrosophic Hypergroupjj, to appear in International Journal of Neutrosophic Science (IJNS).

[18]     Kyung Ho Kim, Davvaz, B. and Eun Hwan Roh, jjOn Hyper R-Subgroups of Hypernear-ringsjj, Scientiae Mathematicae Japonicae Online, pp. 649–656, 2007.

[19]     Mittas, J., jjHypergroupes canoniquesjj, Mathematica Balkanica, Vol.2, pp.165-179, 1972.

[20]     Mittas, J., jjHyperanneaux et certaines de leurs proprietesjj, Vol.269, pp. A623-a626, 1969.

[21]     Massouros, C., jjSome properties of certain Subhypergroupsjj, RATIO MATHEMATICA Vol.25, pp.67- 76, 2013.

[22]     Smarandache, F., jj(T,I,F)- Neutrosophic Structuresjj, Neutrosophic Sets and Systems,Vol. 8, pp. 3-10, 2015.

[23]     Stratisgopoulos, D., jjCertaines classes d’hypercorps et d’hyperanneaux, in Hypergroups, Other Multi- valued Structures and Their Applicationsjj, University of Udine, Udine, Italy, pp. 105-110, 1985.

[24]     Vasantha  Kandasamy  W.B   and   Smarandache,F.,   jjBasic   Neutrosophic   Algebraic   Structures   and Their Applications to Fuzzy and Neutrosophic Modelsjj, Hexis, Church Rock, 2004, http://fs.gallup.unm.edu/eBook-otherformats.htm

[25]     Vasantha  Kandasamy,  W.B.  and  Florentin  Smarandache,  jjSome  Neutrosophic  Algebraic  Structures and Neutrosophic N-Algebraic Structuresjj, Hexis, Phoenix, Arizona, 2006, http://www.gallup.unm.edu/smarandache/eBooks-otherformats.htm.

[26]     Vasantha Kandasamy, W.B., jjNeutrosophic Ringsjj, Hexis, Phoenix, Arizona, 2006, http://www.gallup.unm.edu/ smarandache/eBooks-otherformats.htm.