International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

Submit Your Paper

2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 18 , Issue 3 , PP: 93-113, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

2-Absorbing Neutrosophic Weakly Completely Γ-Ideals

Serkan Onar 1 *

  • 1 Department of Mathematical Engineering, Yildiz Technical University, Davutpas¸a-Istanbul, Turkey - (serkan10ar@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.180308

    Received: January 28, 2022 Accepted: April 17, 2022
    Abstract

    The goal of this study is to present a definition of a generalization of neutrosophic prime Γ-ideals in Γ-rings by introducing 2-absorbing neutrosophic weakly completely Γ-ideals of commutative Γ-rings and to propose their properties. Also, we give the notion of 2-absorbing K- Γ-neutrosophic ideals of Γ-rings. Moreover, we acquire a scheme that relationship between definition of 2-absorbing neutrosophic weakly completely Γ-ideals and 2-absorbing K- Γ-neutrosophic ideals of Γ-rings. Finally, we investigate neutrosophic quotient Γ-ring of  induced by the 2-absorbing neutrosophic weakly completely Γ-ideal is a 2-absorbing Γ− ring.

    Keywords :

    2-absorbing, 2-absorbing neutrosophic weakly completely &Gamma , -ideal, 2-absorbing K-neutrosophic &Gamma , -ideal

      ,

    References

    [1] Smarandache, F., “A unifying field in logics: Neutrosophy Logic. Neutrosophy, Neutrosophic Probability, Set and Statistics”, American esearch, ehoboth 1998.

    [2] Kandasamy, V.W.B., and Smarandache, F., “Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures”, Hexis, Phonex, Arizona 2006.

    [3] Shabir, M., Ali, M., Naz, M., and Smarandache, F., “Soft Neutrosophic Group”, Neutrosophic Sets and Systems, Vol.1, pp. 13-25, 2013.

    [4] Wang, H., Smarandache, F., Zhang, Y., Sunderraman ., “Single Valued Neutrosophic Sets”, Proc. of 10th Int. Conf. on Fuzzy Theory and Technology, Salt Lake City, Utah, July 21-26, 2005.

    [5] Cetkin, V., Varol, B.P. and Aygun,¨ H., “On Neutrosophic Submodules Of A Module, Hacettepe Journal of Mathematics and Statistics, Vol. 46(5), pp. 791-799, 2017.

    [6] Majumdar, P., and Samanta, S.K., “On Similarity And Entropy Of Neutrosophic Sets”, Journal of Intel-ligent and Fuzzy Systems, Vol. 26(3), pp. 1245-1252, 2014.

    [7] Salama, A.A., and Al-Blowi, S.A., “Neutrosophic Set And Neutrosophic Topological Spaces”, Iosr Jour-nal of Mathematics, Vol. 3(4), pp. 31-35, 2012.

    [8] Olgun, N., and Hatip, A., “On efined Neutrosophic -module”, IJNS, Vol. 7(2), pp. 87-96, 2020.

    [9] Nobusawa, N., “On A Generalization Of The ing Theory”, Osaka Journal Of Mathematics, Vol.1, pp. 81-89, 1964.

    [10] Barnes, W.E., “On The Γ− ings Of Nobusawa”, Pacific Journal Of Mathematics, Vol. 18, pp. 411-422, 1966.

    [11] Kyuno, S., “A Gamma ing With The ight And Left Unities”, Mathematica Japonica, Vol. 24(2), pp. 191-193, 1979.

    [12] Kyuno, S., “On Prime Gamma ings”, Pacific Journal of Mathematics, Vol. 75(1), pp. 185-190, 1978.

    [13] Luh, J., “On The Theory Of Simple Γ− ings”, Michigan Mathematics Journal, Vol. 16, pp. 65-75, 1969.

    [14] Badawi, A., “On 2-Absorbing Ideals Of Commutative ings”, Bulletin of the Australian Mathematical Society, Vol. 75, pp. 417-429, 2007.

    [15] Anderson, D.F., and Badawi, A., “On n-Absorbing Ideals Of Commutavie ings”, Commutative Algebra, Vol. 39, pp. 1646-1672, 2011.

    [16] Badawi, A., Tekir, U., Yetkin, E., “On 2-Absorbing Primary Ideals In Commutative ings”, Bulletin of the Australian Mathematical Society, Vol. 51(4), pp. 1163-1173, 2014.

    [17] Badawi, A., and Darani, A.Y., “On Weakly 2-Absorbing Ideals Of Commutative ings”, Houston Journal of Mathematics, Vol. 39, pp. 441-452, 2013.

    [18] Darani, A.Y., and Puczylowski, E. ., “On 2-Absorbing Commutative Semigroups And Their Applica-tions To ings”, Semigroup Forum, Vol. 86, pp. 83-91, 2013.

    [19] Kumar, P., Dubey, M.K., and Sarohe, P., “Some esults On 2-Absorbing Ideals In Commutative Semir-ings”, Journal of Mathematics and Applications, Vol. 38, pp. 77-84, 2015.

    [20] Darani, A.Y., “On L−fuzzy 2-Absorbing Ideals”, Italian Journal of Pure and Applied Mathematics, Vol. 36, pp. 147-154, 2016.

    [21] Darani, A.Y., and Hashempoor, A., “L−fuzzy 0-(1- or 2- or 3-) 2-Absorbing Ideals In Semiring”, Annals of Fuzzy Mathematics and Informatics, Vol. 7(2), pp. 303-311, 2014.

    [22] Sonmez,¨ D., Yes¸ilot, G., Onar, S., Ersoy, B.A., and Davvaz, B., “On 2-Absorbing Primary Fuzzy Ideals of Commutative ings”, Mathematical Problems in Engineering, Vol. 2017, Article ID 5485839.

    [23] Dutta, T.K., and Chanda, T., “Structures Of Fuzzy Ideals Of Γ− ing”, Bulletin of the Malaysian Math-ematical Sciences Society, Vol. 28, pp. 9-18, 2005.

    [24] Onar, S., Sonmez, D., Ersoy, B.A., Yesilot, G., Hila, K., “A Study On Fuzzy 2-Absorbing Primary Γ-Ideals In Γ- ings”, Filomat, Vol. 31(18), pp. 5753–5767, 2017.

    [25] Yella, B., Akbar ., “On Neutrosophic Γ-Semirings”, Neutrosophic Set and Systems, Vol. 47, pp. 338-353, 2021.

    Cite This Article As :
    Onar, Serkan. 2-Absorbing Neutrosophic Weakly Completely Γ-Ideals. International Journal of Neutrosophic Science, vol. , no. , 2022, pp. 93-113. DOI: https://doi.org/10.54216/IJNS.180308
    Onar, S. (2022). 2-Absorbing Neutrosophic Weakly Completely Γ-Ideals. International Journal of Neutrosophic Science, (), 93-113. DOI: https://doi.org/10.54216/IJNS.180308
    Onar, Serkan. 2-Absorbing Neutrosophic Weakly Completely Γ-Ideals. International Journal of Neutrosophic Science , no. (2022): 93-113. DOI: https://doi.org/10.54216/IJNS.180308
    Onar, S. (2022) . 2-Absorbing Neutrosophic Weakly Completely Γ-Ideals. International Journal of Neutrosophic Science , () , 93-113 . DOI: https://doi.org/10.54216/IJNS.180308
    Onar S. [2022]. 2-Absorbing Neutrosophic Weakly Completely Γ-Ideals. International Journal of Neutrosophic Science. (): 93-113. DOI: https://doi.org/10.54216/IJNS.180308
    Onar, S. "2-Absorbing Neutrosophic Weakly Completely Γ-Ideals," International Journal of Neutrosophic Science, vol. , no. , pp. 93-113, 2022. DOI: https://doi.org/10.54216/IJNS.180308