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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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Continuous publication

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Open access journal. All articles are freely available online with no APC.

International Journal of Neutrosophic Science
Full Length Article

Volume 3Issue 1PP: 44-53 • 2020

Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra

Madeleine Al- Tahan 1* ,
Bijan Davvaz 2
1Department of Mathematics, Lebanese International University, Bekaa, Lebanon
2Department of Mathematics Yazd University, Yazd, Iran
* Corresponding Author.
verified

Open Access & Copyright

© 2020 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Abstract

The connection between neutrosophy and algebra has been of great interest with respect to many researchers. The objective of this paper is to provide a connection between neutrosophic −structures and subtraction algebras. In this regard, we introduce the concept of neutrosophic −ideals in subtraction algebra. Moreover, we study its properties and find a necessary and sufficient condition for a neutrosophic −structure to be a neutrosophic −ideal.

Keywords

Subtraction algebra &nbsp &alefsym &minus structure Neutrosophic&nbsp &alefsym &minus ideal Level set

References

[1] Al- Tahan, M., “Some results on single valued neutrosophic (weak) polygroups”, International Journal of Neutrosophic Science (IJNS), vol 2, no.1, pp. 38-46, 2020. 

 

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

 

[3] Ibrahim, M.A., Agboola, A.A.A., Adeleke, E.O., Akinleye, S.A., “Introduction to neutrosophic subtraction algebra and neutrosophic subtraction semigroup”, International journal of neutrosophic science (IJNS) vol 2 , no. 1, pp. 47-62 ,2020.

 

[4] Jun, Y. B., Kim, H. S, Roh, E. H., “Ideal theory of subtraction algebras”, Sci. Math. Jpn., vol 61, no. 3, pp. 459–464, 2005.

 

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[8] Park, C.H., “Neutrosophic ideal of subtraction algebras”, Neutrosophic Sets and Systems, vol. 24, pp. 36-45, 2019.

 

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[10] Smarandache. F., Neutrosophy: Neutrosophic Probability, Set and logic, Ann Arbor, Michigan, USA, 105 (2002). 

 

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[12] Smarcrandach, F., “NeutroAlgebra is a generalization of partial algebra”, International Journal of Neutrosophic Science,(IJNS), vol. 2, no. 1, pp. 08-17, 2020 

 

[13] Smarcrandach, F., “(t, i, f)-Neutrosophic Structures & I-Neutrosophic Structures (Revisited)”, Neutrosophic Sets and Systems, vol 8, pp. 3-9, 2015.

 

[14] Zadeh, L., “Fuzzy sets”, Inform and Control, vol. 8, pp. 338-353, 1965. 

 

[15] Zelinka, B., “Subtraction semigroups”, Math. Bohemica, vol.120, pp. 445–447, 1995.

Cite This Article

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Tahan, Madeleine Al-, Davvaz, Bijan. "Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra." International Journal of Neutrosophic Science, vol. Volume 3, no. Issue 1, 2020, pp. 44-53. DOI: https://doi.org/10.54216/IJNS.030105
Tahan, M., Davvaz, B. (2020). Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra. International Journal of Neutrosophic Science, Volume 3(Issue 1), 44-53. DOI: https://doi.org/10.54216/IJNS.030105
Tahan, Madeleine Al-, Davvaz, Bijan. "Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra." International Journal of Neutrosophic Science Volume 3, no. Issue 1 (2020): 44-53. DOI: https://doi.org/10.54216/IJNS.030105
Tahan, M., Davvaz, B. (2020) 'Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra', International Journal of Neutrosophic Science, Volume 3(Issue 1), pp. 44-53. DOI: https://doi.org/10.54216/IJNS.030105
Tahan M, Davvaz B. Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra. International Journal of Neutrosophic Science. 2020;Volume 3(Issue 1):44-53. DOI: https://doi.org/10.54216/IJNS.030105
M. Tahan, B. Davvaz, "Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra," International Journal of Neutrosophic Science, vol. Volume 3, no. Issue 1, pp. 44-53, 2020. DOI: https://doi.org/10.54216/IJNS.030105
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