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)
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.
Style | # |
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MLA | Florentin Smarandache, Akbar Rezaei, Hee Sik Kim. "A New Trend to Extensions of CI-algebras." International Journal of Neutrosophic Science, Vol. 5, No. 1, 2020 ,PP. 08-15 (Doi : https://doi.org/10.54216/IJNS.050101) |
APA | Florentin Smarandache, Akbar Rezaei, Hee Sik Kim. (2020). A New Trend to Extensions of CI-algebras. Journal of International Journal of Neutrosophic Science, 5 ( 1 ), 08-15 (Doi : https://doi.org/10.54216/IJNS.050101) |
Chicago | Florentin Smarandache, Akbar Rezaei, Hee Sik Kim. "A New Trend to Extensions of CI-algebras." Journal of International Journal of Neutrosophic Science, 5 no. 1 (2020): 08-15 (Doi : https://doi.org/10.54216/IJNS.050101) |
Harvard | Florentin Smarandache, Akbar Rezaei, Hee Sik Kim. (2020). A New Trend to Extensions of CI-algebras. Journal of International Journal of Neutrosophic Science, 5 ( 1 ), 08-15 (Doi : https://doi.org/10.54216/IJNS.050101) |
Vancouver | Florentin Smarandache, Akbar Rezaei, Hee Sik Kim. A New Trend to Extensions of CI-algebras. Journal of International Journal of Neutrosophic Science, (2020); 5 ( 1 ): 08-15 (Doi : https://doi.org/10.54216/IJNS.050101) |
IEEE | Florentin Smarandache, Akbar Rezaei, Hee Sik Kim, A New Trend to Extensions of CI-algebras, Journal of International Journal of Neutrosophic Science, Vol. 5 , No. 1 , (2020) : 08-15 (Doi : https://doi.org/10.54216/IJNS.050101) |