Volume 3 • Issue 1 • PP: 44-53 • 2020
Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra
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© 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 ℵ−structures and subtraction algebras. In this regard, we introduce the concept of neutrosophic ℵ−ideals in subtraction algebra. Moreover, we study its properties and find a necessary and sufficient condition for a neutrosophic ℵ−structure to be a neutrosophic ℵ−ideal.
Keywords
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.
[5] Jun, Y. B., Lee, K. J. , Song, S. Z., “N-ideals of BCK/BCI-algebras”, J. Chungcheong Math. Soc., vol. 22, pp. 417-437, 2009.
[6] Jun, Y. B., Smarandache. F., Bordbar, H., “Neutrosophic N-structures applied to BCK/BCI-Algebras”, Information, vol.8, no.128, 2017.
[7] Khan, M., Anis, S., Smarandache, F., Jun, Y. B., “Neutrosophic N-structures and their applications in semigroups”, Annals of Fuzzy Mathematics and Informatics, vol. 14, no. 6, pp. 583-598, 2017.
[8] Park, C.H., “Neutrosophic ideal of subtraction algebras”, Neutrosophic Sets and Systems, vol. 24, pp. 36-45, 2019.
[9] Schein, B. M., “Difference Semigroups”, Comm. in Algebra, vol. 20, pp. 2153–2169, 1992.
[10] Smarandache. F., Neutrosophy: Neutrosophic Probability, Set and logic, Ann Arbor, Michigan, USA, 105 (2002).
[11] Smarandache. F., “Neutrosophic set- A generalization of the intuitionistic fuzzy set”. Int. J. Pure Appl. Math., vol 24, pp. 287-297, 2005.
[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.
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