Volume 27, No. 2, pp. 125-138, April 2001

BY

XIANG-YUN XIE

Abstract. We introduce the concepts of the extension of a fuzzy ideal of and 3-prime fuzzy ideal of . We discuss the properties of them and study the relationship between prime ideals of and 3-prime fuzzy ideals of by means of the extensions of fuzzy ideals of . Furthermore, let be commutative. We prove that a 3-prime semiprime fuzzy ideal of can be expressible as the infimum of all prime fuzzy ideals of containing it. As a consequence, if is a semilattice, then a 3-prime fuzzy ideal of is the infimum of prime fuzzy ideals of containing it.

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Received October 02, 1998; revised August 08, 1999; revised December 18.

AMS Subject Classification. 04A72, 20M12.

*Key words*.
fuzzy ideal; fuzzy ideal extension, prime fuzzy ideal, semiprime fuzzy ideal,
3-prime fuzzy ideal.
This reseach was supported by the NNSF of P. R. China and Guangdong
Provincial NSF of P. R. China. The author wishes to thank Prof. Niovi
Kehayopulu and Dr. M. Tsingelis whose
suggestions improved the paper greatly.