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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 5 , Issue 1 , PP: 08-15, 2020 | Cite this article as | XML | Html | PDF | Full Length Article

A New Trend to Extensions of CI-algebras

Florentin Smarandache 1 * , Akbar Rezaei 2 , Hee Sik Kim 3

  • 1 Department of Mathematics & Sciences, University of New Mexico, Gallup, NM 87301, USA - (smarand@unm.edu)
  • 2 Department of Mathematics, Payame Noor University, P.O. Box. 19395-3697, Tehran, Iran - (rezaei@pnu.ac.ir)
  • 3 Department of Mathematics, Hanyang University, Seoul 04763, Korea - (heekim@hanyang.ac.kr)

    • Doi: https://doi.org/10.54216/IJNS.050101

    Abstract

    In this paper, as an extension of CI-algebras, we discuss the new notions of Neutro-CI-algebras and Anti-CI-algebras. First, some examples are given to show that these definitions are different. We prove that any proper CI-algebra is a Neutro-BE-algebra or Anti-BE-algebra. Also, we show that any NeutroSelf-distributive and AntiCommutative CI-algebras are not BE-algebras.  

    Keywords :

    CI-algebra, Neutro-CI-algebra, Anti-CI-algebra, Self-distributive, NeutroSelf-distributive, AntiSelf-distributive, Commutative, NeutroCommuative, AntiCommutative.

    References

    [1]       H.S. Kim, Y.H. Kim, On BE-algebras, Sci. Math. Jpn. vol. 66, no. 1, pp. 113-117, 2007.

    [2]       B.L. Meng, CI-algebras, Sci. Math. Jpn. vol. 71, no. 1, pp. 11–17, 2010. 

    [3]       B.L. Meng, Atoms in CI-algebras and singular CI-algebras, Sci. Math. Jpn. vol. 72, no. 1, pp. 319-324, 2010.

    [4]       B. Piekart, A. Walendziak, On filters and upper sets in CI-algebras, Algebra and Discrete Mathematics, vol. 11, no. 1, pp. 109-115, 2011.

    [5]       A. Rezaei, A. Borumand Saeid, Commutative ideals in BE-algebras, Kyungpook Math. J. vol. 52, pp. 483-494, 2012. Doi:10.5666/KMJ.2012.52.4.483.

    [6]       A. Rezaei, A. Borumand Saeid, R.A. Borzooei, Relation between Hilbert algebras and BE-algebras, Applications and Applied Mathematics, vol. 8, no. 2, pp. 573-584, 2013.

    [7]       A. Rezaei, F. Smarandache, On Neutro-BE-algebras and Anti-BE-algebras, International Journal of Neutrosophic Science, Volume 4 , Issue 1, pp. 08-15 , 2020

    [8]       F. Smarandache, NeutroAlgebra is a Generalization of Partial Algebra, International Journal of Neutrosophic Science (IJNS), vol. 2, no. 1, pp. 8-17, 2020. 

    [9]       F. Smarandache, Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited), Neutrosophic Sets and Systems, vol. 31, pp. 1-16, 2020. DOI: 10.5281/zenodo.3638232.

    [10]     F. Smarandache, Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures, in Advances of Standard and Nonstandard Neutrosophic Theories, Pons Publishing House Brussels, Belgium, Ch. 6, pp. 240-265, 2019. http://fs.unm.edu/AdvancesOfStandardAndNonstandard.pdf. 

    [11]     A. Walendziak, On commutative BE-algebras, Sci. Math. Jpn. vol. 69, pp. 585-588, 2008.

    [12]     X. Zhang, X. Wu, F. Smarandache, M. Hu, Left (Right)-Quasi Neutrosophic Triplet Loops (Groups) and Generalized BE-algebras, Symmetry, 2018,10, 241. DOI: 10.3390/sym10070241.

    Cite This Article As :
    Smarandache, Florentin. , Rezaei, Akbar. , Sik, Hee. A New Trend to Extensions of CI-algebras. International Journal of Neutrosophic Science, vol. , no. , 2020, pp. 08-15. DOI: https://doi.org/10.54216/IJNS.050101
    Smarandache, F. Rezaei, A. Sik, H. (2020). A New Trend to Extensions of CI-algebras. International Journal of Neutrosophic Science, (), 08-15. DOI: https://doi.org/10.54216/IJNS.050101
    Smarandache, Florentin. Rezaei, Akbar. Sik, Hee. A New Trend to Extensions of CI-algebras. International Journal of Neutrosophic Science , no. (2020): 08-15. DOI: https://doi.org/10.54216/IJNS.050101
    Smarandache, F. , Rezaei, A. , Sik, H. (2020) . A New Trend to Extensions of CI-algebras. International Journal of Neutrosophic Science , () , 08-15 . DOI: https://doi.org/10.54216/IJNS.050101
    Smarandache F. , Rezaei A. , Sik H. [2020]. A New Trend to Extensions of CI-algebras. International Journal of Neutrosophic Science. (): 08-15. DOI: https://doi.org/10.54216/IJNS.050101
    Smarandache, F. Rezaei, A. Sik, H. "A New Trend to Extensions of CI-algebras," International Journal of Neutrosophic Science, vol. , no. , pp. 08-15, 2020. DOI: https://doi.org/10.54216/IJNS.050101

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