### Homomorphism and quotient of fuzzy k-hyperideals

#### Abstract

In [15], we introduced the notion of weak (resp. strong) fuzzy k- hyperideal. In this note we investigate the behavior of them under homomorphisms of semihyperrings. Also we define the quotient of fuzzy weak (resp. strong) k-hyperideals by a regular relation of semihyperring and obtain some results.

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R. Ameri and M.M. Zahedi "Hyperalgebraic System", Italian Journal of Pure and Applied Mathematics, 6: (1999) 21-32.

R. Ameri, "Fuzzy Transposition Hypergroups", Italian Journal Pure and Applid Mathematics, No. 18 (2005), 167-174.

R. Ameri and M.M. Zahedi "Hypergroup and join spaces induced by a fuzzy subset",J. PU.M.A, 8: (1997) 155-168.

R. Ameri "Fuzzy (Co-)Norm Hypervector Spaces", Proceedings of the 8th International Congress in Algebraic Hyperstructures and Applications, Samotraki, Greece, September 1-9 (2002) ,71-79.

R. Ameri and M.M. Zahedi "Fuzzy Subhypermodules over fuzzy hyper-rings", Sixth International Congress on AHA, Prague Czech Republic September 1996, Democritus Univ. Press, 1-14.

S. I. Baik, H. S. Kim "On Fuzzy k-Ideals in semirings", Kangweon-Kyungki Math. Jour. 8 (2000) 147-154.

P. Corsini "Prolegomena of Hypergroup Theory", second eddition Aviani, editor (1993).

P. Corsini and V. Leoreanu , "Applications of Hyperstructure Theory", Kluwer Academic Publications (2003).

P. Corsini and V. Leoreanu , "Fuzzy sets and Join Spaces Associated with rough sets", Rend. Circ. Mat., Palermo, 51: (2002) 527-536.

P. Corsini and I. Tofan ," On Fuzzy Hypergroups" J. PU.M.A., 8: (1997) 29-37.

B. Davvaz "Fuzzy Hv- submodules", Fuzzy Sets and Systems, 117: (2001) 477-484.

B. Davvaz "Fuzzy Hv-groups", Fuzzy Sets and Systems, 101: (1999) 191-195.

T. K. Dutta, B.K. Biswas , "Fuzzy Prime ideals of semirings", Bull. Malaysian math. Soc. 17: (1994) 9-16.

T. K. Dutta, B.K. Biswas , "Fuzzy Ideals of Semirings", Bull. Calcutta Math. Soc. 87: (1995) 91-96.

H. Hedayati and R. Ameri, "Fuzzy k-Hyperideals ", Int. J. Pu. Appl. Math. Sci., Vol. 2, No. 2, 247-256.

Y. B. Jun, J. Neggers and H. S. Kim , "On L-fuzzy Ideals in Semirings I", Czech. Math. J. 48: (1998) 669-675.

G. J. Klir, T.A Folger , "Fuzzy Sets, Uncertainties, and Information", Prantice Hall, Englewood Clif and only ifs, NJ (1998).

M. Krasner , "Approximation des Corps Values Complets de Caracter-istque P 6= 0 Par Ceux de Caracteristique 0", Actes due Colloqued; Algebre Superieure C.B.R.M, Bruxelles (1965) 12-22.

V. Leoreanu , "Direct Limit and inverse limit of Join Spaces Associated with Fuzzy Sets", Pure Math. Appl., 11: (2000) 509-512.

W. J. Liu , "Fuzzy Invariants Subgroups and fuzzy Ideals", Fuzzy Sets and Systems, 8: (1987) 133-139.

H.V. Kumbhojkar and M.S. Bapta , "Correspondence Theorem of Fuzzy Ideals", Fuzzy Sets and Systems 41: (1991) 213-219.

D.S. Malik and J. N. Mordeson , "Extension s of fuzzy Subrings and Fuzzy Ideals", Fuzzy Sets and Systems 45: (1992) 245-251.

F. Marty , Surnue generaliz-ation de la notion de group, 8iem course Math. Scandinaves Stockholm (1934) 45-49.

R. Rosenfeld , "fuzzy groups", J. Math. Anal. Appl., 35: (1971) 512-517.

T. Vougiuklis , Hyperstructures and their representations, Hardonic, Press, Inc (1994).

L. A. Zadeh , "Fuzzy Sets", Inform. and Control, vol. 8 (1965) 338-353.

M.M. Zahedi , M. Bolurian, A. Hasankhani, "On polygroups and Fuzzy subpolygroups", J. of Fuzzy Mathematics, No.1, (1995) 1-15.

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