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L-FUZZY SEMI-PRIME IDEALS IN UNIVERSAL ALGEBRAS

  • Received : 2018.11.26
  • Accepted : 2019.03.18
  • Published : 2019.06.30

Abstract

In this paper, we introduce the notion of L-fuzzy semi-prime ideals and the radical of L-fuzzy ideals in universal algebras and make a theoretical study on their basic properties.

Keywords

References

  1. B. A. Alaba and G. M. Addis, L-Fuzzy ideals in universal algebras, Ann. Fuzzy Math. Inform. 17 (1), (2019) 31-39. https://doi.org/10.30948/afmi.2019.17.1.31
  2. B. A. Alaba and G. M. Addis, L-Fuzzy prime ideals in universal algebras, Adv. Fuzzy Syst., 2019 Article ID 5925036 (2019).
  3. P. Agliano, The prime spectrum of a universal algebra, Rivista di Mat. Pura ed AppL 4 (1989), 83-91.
  4. P. Agliano and A. Ursini, Cosets in universal algebra, J. of Algebra 107 (1987), 376-384. https://doi.org/10.1016/0021-8693(87)90094-9
  5. P. Agliano and A. Ursini, Ideals and other generalizations of congruence classes, J. Austral. Math. Soc. 53 (1992), 103-115. https://doi.org/10.1017/S1446788700035436
  6. P. Agliano and A. Ursini, On some ideal basis theorems, Rapporto Matematico n.182, Universita di Siena (1988).
  7. Y. Bo and W. Wu, Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems 35 (1990), 231-240. https://doi.org/10.1016/0165-0114(90)90196-D
  8. S. Burris and H. P. Sankappanavor, A Course in Universal Algebra, Springer-Verlag, GTM78, 1981
  9. J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18 (1967) 145-174. https://doi.org/10.1016/0022-247X(67)90189-8
  10. G. Gratzer, Universal algebras, Van Nostrand, Princeton, N. J., (1968).
  11. H. P. Gumm and A. Ursini, 'Ideals in Universal Algebra', Algebra Universalis 19 (1984), 45-54. https://doi.org/10.1007/BF01191491
  12. G. Janelidze, L. Mrki and A. Ursini, Ideals and clots in universal algebra and in semi-abelian categories, J. Algebra 307 (2007), 191-208 https://doi.org/10.1016/j.jalgebra.2006.05.022
  13. A. K. Katsaras and D.B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J. Math. Anal. Appl. 58 (1977) 135-146. https://doi.org/10.1016/0022-247X(77)90233-5
  14. W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982) 133-139. https://doi.org/10.1016/0165-0114(82)90003-3
  15. C. V. Negoita and D.A. Ralescu, Application of Fuzzy Systems Analysis, Birkhauser, Basel, 1975.
  16. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
  17. U. M. Swamy and K. L. N. Swamy, Fuzzy prime ideals of rings, J. Math. Anal. Appl. 134 (1988), 94-103. https://doi.org/10.1016/0022-247X(88)90009-1
  18. U. M. Swamy and D. V. Raju, Algebraic fuzzy systems, Fuzzy Sets and Systems 41 (1991), 187-194. https://doi.org/10.1016/0165-0114(91)90222-C
  19. U. M. Swamy and D. V. Raju, Irreducibility in algebraic fuzzy systems, Fuzzy Sets and Systems 41 (1991), 233-241. https://doi.org/10.1016/0165-0114(91)90227-H
  20. U. M. Swamy and D. V. Raju, Fuzzy ideals and congruences of lattices, Fuzzy Sets and Systems 95 (1998), 249-253. https://doi.org/10.1016/S0165-0114(96)00310-7
  21. A. Ursini, Prime ideals in universal algebras, Acta Universitatis Carolinae. Mathematica et Physica 25, (1984) 75-87.
  22. C. K. Wong, Fuzzy point and local properties of fuzzy topology, J. Math. Anal. Appl. 46 (1974), 316-328. https://doi.org/10.1016/0022-247X(74)90242-X
  23. L. A. Zadeh, Fuzzy Sets, Inform. and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X

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  1. FUZZY PRIME SPECTRUM OF C-ALGEBRAS vol.28, pp.1, 2019, https://doi.org/10.11568/kjm.2020.28.1.49