Fuzzy ideals and fuzzy semiprime ideals: Some ring theoretic analogues (Q1194809)

The author contributes to the straightforward fuzzification of the concept ideal in a ring. Some interesting analogues of the classical results are obtained: -- The fuzzy nil radical of the \(n\)th power of a fuzzy prime ideal equals itself. -- Under rather general supplementary conditions it is shown that a fuzzy ideal of a ring is fuzzy primary if its fuzzy nil radical is a fuzzy maximal ideal of this ring. -- There exists a one-to-one correspondence between the set of all \(f\)-invariant fuzzy semiprime ideals of a ring \(R\) and the set of all fuzzy semiprime ideals of a ring \(R'\) where \(f\) denotes a surjective homomorphism between \(R\) and \(R'\).