Fuzzy prime ideals and fuzzy radical ideals

Information Sciences

Volume 50, Issue 2, March 1990, Pages 111-122

Some properties of the fuzzy prime ideals and radical ideals are studied. Also we study the structure of fuzzy principal ideals.

Wang-jin Liu
Fuzzy invariant subgroup and fuzzy ideals
Internat. J. Fuzzy Sets and Systems
(1982)
Wang-jin Liu
Operations on fuzzy ideals
J. Fuzzy Sets and Systems
(1983)

There are more references available in the full text version of this article.

Spectrum of prime fuzzy ideals
1994, Fuzzy Sets and Systems
A topological space called a spectrum of prime fuzzy ideals and denoted by Fspec(R) is obtained by introducing a topology on the set of prime fuzzy ideals of a ring R. The prime fuzzy ideals used here (introduced by the author elsewhere), are not necessarily two valued, the topology introduced is compact and the usual (nonfuzzy) prime spectrum Spec(R) is a subspace of Fspec(R) and dense in it. Situations under which fuzzy spectrums of different rings are homeomorphic are discussed. In particular, Fspec(R) is proved to be homeomorphic to Fspec(R/Frad(R)), where Frad(R) is the fuzzy prime radical of R.
The correspondence associating a ring R to the topological space Fspec(R) is shown to define a contravarient functor from the category of rings with unity, into the category of compact topological spaces.
On the fuzzy radical of a fuzzy ideal
1993, Fuzzy Sets and Systems
Intuitionistic Fuzzy primary ideal and its homomorphism
2015, Liaoning Gongcheng Jishu Daxue Xuebao (Ziran Kexue Ban)/Journal of Liaoning Technical University (Natural Science Edition)

^☆: Projects supported by the Science Fund of the Chinese Academy of Sciences.