ON PRODUCT OF FUZZY SEMIPRIME IDEALS IN -LA-SEMIGROUPS

Abstract

The purpose of this paper is to introduce the notion of a weakly fuzzy quasi-semiprime ideals in $\Gamma$-LA-semigroups, we study direct product of fuzzy semiprime, fuzzy weakly completely semiprime, weakly fuzzy semiprime and weakly fuzzy quasi-semiprime ideals in $\Gamma$-LA-semigroups. Some characterizations of weakly fuzzy semiprime and weakly fuzzy quasi-semiprime ideals are obtained. Moreover, we investigate relationships between fuzzy weakly completely semiprime and weakly fuzzy quasi-semiprime ideals in $\Gamma$-LA-semigroups.

Keywords

• fuzzy semiprime,fuzzy quasi-semiprime,fuzzy weakly completely semiprime,weakly fuzzy semiprime,weakly fuzzy quasi-semiprime.

References

1. S. Abdullah, M. Aslam, M. Imran and M. Ibrar, Direct product of intuitionistic fuzzy sets in LA-semigroups-II, Annals of Fuzzy Mathematics and Informatics, 2 (2) (2011), 151 - 160.
2. S. Abdullaha, M. Aslama and M. Naeemb, Intuitionistic fuzzy Bi- -ideals of -LA-semigroups, International Journal of Algebra and Statistics, 1(2)(2012), 46 - 54.
3. S. Abdullah and M. Alsam, On intuitionistic fuzzy prime -Ideals of -LA-semigroups, J. Appl. Math. and Informatics, 30(3 - 4)(2012), 603 - 612.
4. M. Aslam, S. Abdullah and M. Nasreen, Direct product of intuitionistic fuzzy sets in LA-semigroups, Fuzzy Sets, Rough Sets and Multivalued Operations Applications, 3(1)(2011), 1 - 9.
5. M.A. Kazim and M. Naseeruddin, On almost semigroups, The Alig. Bull. Math., 2(1972), 1 - 7.
6. M. Khan, S. Anis and Faisal, On fuzzy -ideals of -Abel-Grassmann's groupoids, Research Journal of Applied Sciences, Engineering and Technology, 6(8)(2013), 1326 - 1334.
7. M. Khan, S. Anis and S. Lodhi, A study of fuzzy Abel-Grassmann' s groupoids, International Journal of the Physical Sciences, 7(4)(2012), 584 - 592.
8. M. Khan, Y. Bae Jun and T. Mahmood, Generalized fuzzy interior ideals in Abel Grassmann's groupoids, Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences, 2010, 1 - 14.

9. M. Khan, Y. Bae Jun and F. Yousafzai, Fuzzy ideals in right regular LA-semigroups, Hacettepe Journal of Mathematics and Statistics, 44 (3)(2015), 569 - 586.
10. M. Khan and Faisal, On fuzzy ordered Abel-Grassmann's groupoids, Journal of Mathematics Research, 3 (2)(2011), 27 - 40.
11. M. Khan, M. Faisal Iqbal and M. Nouman A. Khan, On anti fuzzy ideals in left almost semigroups, Journal of Mathematics Research, 2 (3)(2010), 203 - 210.
12. M. Khan and M.N. Khan, On fuzzy Abel Grassmann's groupoids, Advance in Fuzzy Math., 5(3)(2010), 349 - 360.
13. M. Khan and M. Nom an Aslam Khan, Fuzzy Abel-Grassmann's groupoids, arXiv:0904.0077v1 [math.GR], (2009).
14. N. Kuroki, Fuzzy semiprime quasi ideals in semigroups, Inform. Sci., 75 (3)(1993), 201 - 211.
15. J.N. Mordeson, Fuzzy semigroups, Springer-Verlag Berlin Heidelberg, (2003).
16. V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci., 158(2004), 277 - 288.
17. Q. Mushtaq and M. Khan, A note on an Abel-Grassmann's 3-band, Quasigroups and Related Systems, 15(2007), 295 - 301.
18. Q. Mushtaq and M. Khan, Direct product of Abel Grassmann's groupoids, J. Interdiscip. Math., 11(2008), 461 - 467.
19. Q. Mushtaq and M. Khan, Ideals in left almost semigroup, arXiv:0904.1635v1 [math.GR], (2009).
20. Q. Mushtaq and SM. Yousuf, On LA-semigroups, TheAlig. Bull. Math., 8(1978), 65 - 70.
21. Q. Mushtaq and S.M. Yousuf, On LA-semigroup defined by a commutative inverse semigroup, Math. Bech, 40(1988), 59 - 62.
22. M. Naseeruddin, Some studies in almost semigroups and flocks, Ph.D. thesis: Aligarh Muslim University: Aligarh: India, (1970).
23. M.K. Sen, On -semigroups, Proceeding of International Symposium on Algebra and Its Applications, Decker Publication: New York, (1981), 301 - 308.
24. T. Shah, Inayatur-Rehman and A. Khan, Fuzzy -ideals in -AG-groupoids, Hacettepe Journal of Mathematics and Statistics, 43(4)(2014), 625 - 634.
25. T. Shah and I. Rehman, Decomposition of locally associative -AG-groupoids, Novi Sad J. Math., 43(1)(2013), 1 - 8.
26. F. Yousafzai, N. Yaqoob, S. Haq and R. Manzoor, A note on intuitionistic fuzzy -LA-semigroups, World Applied Sciences Journal, 19(12)(2012), 1710 - 1720.
27. L.A. Zadeh, Fuzzy sets, Inform. Control, 8(1965), 338 - 353.