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NEUTROSOPHIC IDEALS IN SUBTRACTION ALGEBRAS

  • Kim, Young Hie (Bangmok College of General Education, Myongji University Yongin Campus (Natural Sciences Campus)) ;
  • Ahn, Sun Shin (Department of Mathematics Education, Dongguk University)
  • Received : 2018.12.09
  • Accepted : 2019.03.27
  • Published : 2019.06.25

Abstract

The notions of a neutrosophic subalgebra and a neutrosohic ideal of a subtraction algebra are introduced. Characterizations of a neutrosophic subalgebra and a neutrosophic ideal are investigated. We show that the homomorphic preimage of a neutrosophic subalgebra of a subtraction algebra is a neutrosophic subalgebra, and the onto homomorphic image of a neutrosophic subalgebra of a subtraction algebra is a neutrosophic subalgebra.

Keywords

References

  1. J. C. Abbott, Sets, Lattices and Boolean Algebras, Allyn and Bacon, Boston, 1969.
  2. S. S. Ahn and Y. H. Kim, Quotient subtraction algebras by an int-soft ideal, J. Comput. Anal. Appl. 25 (2018), 728-737.
  3. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and Systems 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
  4. Y. B. Jun and H. S. Kim, On ideals in subtraction algebras, Sci. Math. Jpn. Online, e-2006 (2006), 1081-1086.
  5. Y. B. Jun, H. S. Kim and E. H. Roh, Ideal theory of subtraction algebras, Sci. Math. Jpn. Online, e-2004 (2004), 397-402.
  6. Y. B. Jun, Y. H. Kim and K. A. Oh, Subtraction algebras with additional conditions, Commun. Korean Math. Soc. 22 (2007), 1-7. https://doi.org/10.4134/CKMS.2007.22.1.001
  7. Y. B. Jun, F. Smarandache and H. Bordbar, Neutrosophic ${\mathscr{N}}$-structures applied to BCK/BCI-algebras, Information, (to submit).
  8. B. M. Schein, Difference Semigroups, Comm. Algebra 20 (1992), 2153-2169. https://doi.org/10.1080/00927879208824453
  9. F. Smarandache, Neutrosophy, Neutrosophic Probablity, Sets, and Logic, Amer. Res. Press, Rehoboth, USA, 1998.
  10. L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  11. B. Zelinka, Subtraction Semigroups, Math. Bohemica 120 (1995), 445-447. https://doi.org/10.21136/MB.1995.126093