Geodesic
Fuzzy ideals extenstions of ordered semigroups
Lobachevskii journal of mathematics, Tome 19 (2005), pp. 29-40.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we introduce the concepts of the extension of fuzzy ideals , prime, semiprime and 3-prime fuzzy ideals in an ordered semigroup $S$, respectively. We discuss properties of fuzzy ideals extensions and the relationships between prime fuzzy ideals and 3-prime fuzzy ideals of $S$ in terms of the extension of fuzzy ideals of $S$, we give an example to show that 3-prime fuzzy ideal is not necessarily prime. Moreover, for commutative ordered semigroups, we obtain some properties of the extension of fuzzy ideals in commutative ordered semigroup.
Keywords: fuzzy ideals extension, ordered semigroup, prime fuzzy ideals, semiprime fuzzy ideals, 3-prime fuzzy ideals. 
@article{LJM_2005_19_a2,
     author = {X.-Yu. Xie and F. Yan},
     title = {Fuzzy ideals extenstions of ordered semigroups},
     journal = {Lobachevskii journal of mathematics},
     pages = {29--40},
     publisher = {mathdoc},
     volume = {19},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2005_19_a2/}
}
TY  - JOUR
AU  - X.-Yu. Xie
AU  - F. Yan
TI  - Fuzzy ideals extenstions of ordered semigroups
JO  - Lobachevskii journal of mathematics
PY  - 2005
SP  - 29
EP  - 40
VL  - 19
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2005_19_a2/
LA  - en
ID  - LJM_2005_19_a2
ER  - 
%0 Journal Article
%A X.-Yu. Xie
%A F. Yan
%T Fuzzy ideals extenstions of ordered semigroups
%J Lobachevskii journal of mathematics
%D 2005
%P 29-40
%V 19
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2005_19_a2/
%G en
%F LJM_2005_19_a2
X.-Yu. Xie; F. Yan. Fuzzy ideals extenstions of ordered semigroups. Lobachevskii journal of mathematics, Tome 19 (2005), pp. 29-40. http://geodesic.mathdoc.fr/item/LJM_2005_19_a2/

[1] Xiang-Yun Xie, “Fuzzy ideals extensions of semigroups”, Soochow Journal of Mathematics, 27 (2001), 125–138 | MR | Zbl

[2] Xiang-Yun Xie, Introduction to Theory of Ordered Semigroups, Kexue Press, Beijing, 2001

[3] Xiang-Yun Xie and Ming-Fen Wu, Theory of Fuzzy Semigroups, Kexue Press, Beijing, 2005

[4] Xiang-Yun Xie and Ming-Fen Wu, “On the ideal extensions in ordered semigroups”, Semigroup Forum, 53 (1996), 63–71 | DOI | MR | Zbl

[5] J. Ahsan, K. Saifullah and M. Faid Khan, “Semigroups characterized by their fuzzy ideals”, Fuzzy Systems and Mathematics, 9 (1995), 29–32 | MR

[6] Niovi Kehayopulu, Xiang-Yun Xie and M. Tsingelis, “A characterization of prime and semiprime ideals of semigroups in terms of fuzzy subsets”, Soochow J. Math., 27:2 (2001), 139–144 | MR | Zbl

[7] L. A. Zadeh, “Fuzzy sets”, Inform. Control, 8 (1965), 338–353 | DOI | MR | Zbl

[8] N. Kuroki, “Fuzzy semiprime ideals in semigroups”, Fuzzy sets and systems, 8 (1982), 71–79 | DOI | MR | Zbl

[9] N. Kuroki, “On fuzzy semigroups”, Information Sciences, 53 (1991), 203–236 | DOI | MR | Zbl

[10] T. K. Mukherjee and M. K. Sen, “Prime fuzzy ideals in rings”, Fuzzy sets and systems, 32 (1989), 337–341 | DOI | MR | Zbl

[11] N. Kehayopulu, M. Tsingelis, “Fuzzy bi-ideals in ordered groupoids”, Information Sciences, 171 (2005), 13–28 | DOI | MR | Zbl

[12] N. Kehayopulu, M. Tsingelis, “Fuzzy sets in ordered groupoids”, Semigroup Forum, 65 (2002), 128–132 | DOI | MR | Zbl

[13] N. Kehayopulu, M. Tsingelis, “The embedding of an ordered groupoid into a poe-groupoid in terms of fuzzy sets”, Infom. Sci., 152 (2003), 231–236 | DOI | MR | Zbl