Spectrum of Prime Fuzzy Ideals of A Semigroup
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Date
2005-06
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Addis Ababa University
Abstract
This paper has three parts: The first part deals with preliminaries on semi
groups, spectrum of prime ideals of a semi group and preliminaries on fuzzy sets that are
going to be used for the works in the following parts. In the second part primary fuzzy
ideals, semi prime fuzzy ideals and nil and prime radical of a fuzzy ideal are discussed
and their relationship with prime fuzzy ideals is investigated. It is also proved that the
nil and prime ideals coincide when the grade membership lattice is totally ordered. In
the last, a topological space called spectrum of fuzzy ideals, FSpec(S), is obtained by
introducing a topology on the set of prime fuzzy ideals of a semi group S. It is also
proved that FSpec(S) is compact and the non-fuzzy prime spectrum, Spec(S) , is dense in
FSpec(S). It is shown that if S and S' are isomorphic, then FSpec(S) and FSpec(S') are
homeomorphic.
Key words: Fuzzy ideal, Prime fuzzy ideal, Semi prime fuzzy ideal, Primary fuzzy ideal,
Radical of a fuzzy ideal, Compact topological space.
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Keywords
Fuzzy ideal, Prime fuzzy ideal, Semi prime fuzzy ideal, Primary fuzzy ideal, Radical of a fuzzy ideal, Compact topological space