Volume 3 • Issue 1 • PP: 44-53 • 2020
Neutrosophic ℵ–Ideals (ℵ-Subalgebras) of Subtraction Algebra
View PDF 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.
Cite This Article
Choose your preferred format