A New Trend to Extensions of CI-algebras

Florentin; Akbar; Hee Sik

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

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Volume 5 • Issue 1 • PP: 08-15 • 2020

A New Trend to Extensions of CI-algebras

Florentin Smarandache ^1*

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,

Akbar Rezaei ²

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,

Hee Sik Kim ³

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¹Department of Mathematics & Sciences, University of New Mexico, Gallup, NM 87301, USA

²Department of Mathematics, Payame Noor University, P.O. Box. 19395-3697, Tehran, Iran

³Department of Mathematics, Hanyang University, Seoul 04763, Korea

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.050101

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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

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[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.

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Smarandache, Florentin, Rezaei, Akbar, Kim, Hee Sik. "A New Trend to Extensions of CI-algebras." International Journal of Neutrosophic Science, vol. Volume 5, no. Issue 1, 2020, pp. 08-15. DOI: https://doi.org/10.54216/IJNS.050101

Smarandache, F., Rezaei, A., Kim, H. (2020). A New Trend to Extensions of CI-algebras. International Journal of Neutrosophic Science, Volume 5(Issue 1), 08-15. DOI: https://doi.org/10.54216/IJNS.050101

Smarandache, Florentin, Rezaei, Akbar, Kim, Hee Sik. "A New Trend to Extensions of CI-algebras." International Journal of Neutrosophic Science Volume 5, no. Issue 1 (2020): 08-15. DOI: https://doi.org/10.54216/IJNS.050101

Smarandache, F., Rezaei, A., Kim, H. (2020) 'A New Trend to Extensions of CI-algebras', International Journal of Neutrosophic Science, Volume 5(Issue 1), pp. 08-15. DOI: https://doi.org/10.54216/IJNS.050101

Smarandache F, Rezaei A, Kim H. A New Trend to Extensions of CI-algebras. International Journal of Neutrosophic Science. 2020;Volume 5(Issue 1):08-15. DOI: https://doi.org/10.54216/IJNS.050101

F. Smarandache, A. Rezaei, H. Kim, "A New Trend to Extensions of CI-algebras," International Journal of Neutrosophic Science, vol. Volume 5, no. Issue 1, pp. 08-15, 2020. DOI: https://doi.org/10.54216/IJNS.050101

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