Spectrum Of Prime Fuzzy Ideals Of A Semigroup

This paper has three parts: The first part deals with preliminaries on semirngroups, spectrum of prime ideals of a semi group and preliminaries on fuzzy sets that arerngoing to be used for the works in the following parts. In the second part primary fuzzyrnideals, semi prime fuzzy ideals and nil and prime radical of a fuzzy ideal are discussedrnand their relationship with prime fuzzy ideals is investigated. It is also proved that thernnil and prime ideals coincide when the grade membership lattice is totally ordered. Inrnthe last, a topological space called spectrum of fuzzy ideals, FSpec(S), is obtained byrnintroducing a topology on the set of prime fuzzy ideals of a semi group S. It is alsornproved that FSpec(S) is compact and the non-fuzzy prime spectrum, Spec(S) , is dense inrnFSpec(S). It is shown that if S and S' are isomorphic, then FSpec(S) and FSpec(S') arernhomeomorphic.rnKey words: Fuzzy ideal, Prime fuzzy ideal, Semi prime fuzzy ideal, Primary fuzzy ideal,rnRadical of a fuzzy ideal, Compact topological space.

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