Spectrum of prime fuzzy ideals
An attempt has been made to introduce an appropriate topology on the set of prime fuzzy ideals. Instead of appealing to other definitions of prime fuzzy ideals, as in literature, the author has taken his own definition introduced earlier; such prime fuzzy ideals in a commutative ring \(R\) with identity are denoted by \(F \text{spec} (R)\); the author has studied \(F \text{spec} (R)\) with an appropriate topology and has studied many interesting properties. Situations under which fuzzy spectra of different rings are homeomorphic are discussed; in particular, \(F \text{spec} (R)\) is proved to be homeomorphic to \(F \text{spec} (R/F \text{rad} (R))\), where \(F \text{rad} (R)\) is the fuzzy prime radical of \(R\). The correspondence associating a ring \(R\) to the topological space \(F \text{spec} (R)\) is shown to define a contravariant functor from the category of rings with unity, into the category of compact topological spaces.
scientific article; zbMATH DE number 788364