Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지

SOME FUZZY SEMIPRIME IDEALS OF SEMIGROUPS

  • Kim, Jupil (Department of Mathematics Hannam University)
  • Received : 2009.05.31
  • Accepted : 2009.08.14
  • Published : 2009.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this paper is to study the some properties of fuzzy quasi-semiprime ideal, fuzzy prime ideals and to prove some fundamental properties of semigroups. In particular, we will establish a relation between fuzzy prime ideals and weakly completely semiprime ideals by using the some equivalent conditions of fuzzy semiprime ideals.

Keywords

References

  1. J. Ahsan, K. Saifullah, M. F. Khan, Semigroups characterized by their fuzzy ideals, Fuzzy Systems Math. 9 (1995), 29-32.
  2. A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups Vol I., Math. Surveys No. 7, Am. Math. Soc., Province, RI. 1961
  3. J. M. Howie, An introduction to semigroup theory, Academic Press, 1976.
  4. J. L. Wang, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Set and Systems 8 (1982), 133-139. https://doi.org/10.1016/0165-0114(82)90003-3
  5. N. Kuroki, Fuzzy bi-ideals in semigroups, Comment Math. Univ. St. Pauli. 28 (1979), 17-21.
  6. N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems 5 (1981), 203-215 https://doi.org/10.1016/0165-0114(81)90018-X
  7. N. Kuroki, Fuzzy semiprime ideals in semigroups, Fuzzy Sets and Systems 8 (1982), 71-79. https://doi.org/10.1016/0165-0114(82)90031-8
  8. D. S. Malik, J. N. Mordeson, Fuzzy prime ideals of a ring, Fuzzy Set and Systems 37 (1990), 93-98. https://doi.org/10.1016/0165-0114(90)90066-F
  9. T. K. Mukherjee and M. K. Sen, On fuzzy ideals of a rings I, Fuzzy Sets and Systems 21 (1987), 99-104 https://doi.org/10.1016/0165-0114(87)90155-2
  10. T. K. Mukherjee and M. K. Sen, prime fuzzy ideals in rings, Fuzzy Sets and Systems 32 (1989), 337-341 https://doi.org/10.1016/0165-0114(89)90266-2
  11. M. Petrich, Introduction to semigroups, Charles E. Merrill. Columbus. Oh. 1973
  12. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517 https://doi.org/10.1016/0022-247X(71)90199-5
  13. Xiang-yun Xie, On prime Fuzzy ideals of a semigroups, The J. Fuzzy Math. 8 (2001), no. 1, 231-241
  14. Xiang-yun Xie, On prime, quasi-prime, weakly quasi-prime fuzzy left ideals of semigroups, Fuzzy Sets and Systems 123 (2001), 239-249 https://doi.org/10.1016/S0165-0114(00)00091-9
  15. Xiang-yun Xie, Fuzzy ideals extensions in semigroups, Kyungpook Math. J. 42 (2002), 39-49
  16. L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X