A Novel of Cubic Ideals in Γ-Semigroups

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DOI: https://doi.org/10.28924/2291-8639-20-2022-69
Published: Dec 26, 2022
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Pannawit Khamrot, Thiti Gaketem, A Novel of Cubic Ideals in Γ-Semigroups, Int. J. Anal. Appl., 20 (2022), 69.

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Pannawit Khamrot, Thiti Gaketem

Abstract

In this paper, we give the concepts of new types of cubic ideals in Γ-semigroups. We study properties and relationships between cubic (α, β)-ideals and ideals in semigroups. Furthermore, we proved some basic properties of cubic almost ideals in semigroups.

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References

  1. S. Bashir, A. Sarwar, Characterizations of Γ-Semigroups by the Properties of Their Interval Valued T-Fuzzy Ideals, Ann. Fuzzy Math. Inform. 9 (2015), 441-461.
  2. V. Chinnadaurai, K. Bharathivelan, Cubic Ideal of Γ-Semigroups, Int. J. Current Res. Modern Educ. 1 (2016), 138-150.
  3. R. Chinram, On Quasi-Gamma-Ideals in Gamma-Semigroups, ScienceAsia. 32 (2006), 351-353. https://doi.org/10.2306/scienceasia1513-1874.2006.32.351.
  4. N. Deetae, P. Khamrod, Q-Cubic Bi-Quasi Ideals of Semigroups, Glob. J. Pure Appl. Math. 16 (2020), 553-566.
  5. T. Gaketem, Cubic (1, 2)-Ideals in Semigroups, TWMS J. Appl. Eng. Math. 12 (2022), 1271-1282.
  6. T. Gaketem, Cubic Interior Ideals in Semigroups, Azerbaijan J. Math. 10 (2020), 85-104.
  7. T. Gaketem, A. Iampan, Cubic Filters of Semigroups, Appl. Sci. 24 (2022), 131-141.
  8. A. Hadi, A. Khan, Cubic Generalized Bi-Ideal in Semigroups, Discuss. Math., Gen. Algebra Appl. 36 (2016), 131- 146. https://doi.org/10.7151/dmgaa.1254.
  9. A. Iampan, Note on Bi-Ideal in Γ-Semigroups, Int. J. Algebra. 34 (2009), 181-188.
  10. Y.B. Jun, C.S. Kim, K.O. Yang, Cubic Sets, Ann. Fuzzy Math. Inform. 4 (2012), 83-98.
  11. Y.B. Junand, A. Khan, Cubic Ideals in Semigroups, Honam Math. J. 35 (2013), 607-623. https://doi.org/10.5831/HMJ.2013.35.4.607.
  12. N. Kuroki, Fuzzy Bi-Ideals in Semigroup, Comment. Math. Univ. St. Paul. 28 (1980), 17–21. https://doi.org/10.14992/00010265.
  13. P. Khamrot, T. Gaketem, Cubic bi-quasi ideals of semigroups, J. Discrete Math. Sci. Cryptography. 24 (2021), 1113-1126. https://doi.org/10.1080/09720529.2021.1889777.
  14. P. Kummoon, T. Changphas, Bi-Bases of Γ-Semigroups, Thai J. Math. Special Issue (2017), 75-86.
  15. D. Mandal, Characterizations of Γ-Semirings by Their Cubic Ideals, Int. J. Math. Comput. Sci. 13 (2019), 150-156.
  16. Al. Narayanan, T. Manikantan, Interval-Valued Fuzzy Ideals Generated by an Interval-Valued Fuzzy Subset in Semigroups, J. Appl. Math. Comput. 20 (2006), 455–464. https://doi.org/10.1007/bf02831952.
  17. A. Simuen, A. Iampan, R. Chinram, A Novel of Ideals and Fuzzy Ideals of Γ-Semigroups, J. Math. 2021 (2021), 6638299. https://doi.org/10.1155/2021/6638299.
  18. L.A. Zadeh, Fuzzy Sets, Inform. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  19. L.A. Zadeh, The Concept of a Linguistic Variable and Its Application to Approximate Reasoning–I, Inform. Sci. 8 (1975), 199–249. https://doi.org/10.1016/0020-0255(75)90036-5.