The nil radical of a fuzzy ideal (Q1315863)

Let \(R\) be a commutative ring. The authors define the fuzzy nil radical of an ideal. They then introduce the concept of a fuzzy semiprime ideal of \(R\) with the help of the fuzzy nil radical. A commutative regular ring is characterized by its semiprime ideals. It is shown that the intersection of all fuzzy semiprime ideals of \(R\) which contain a given fuzzy ideal \(\lambda\) is precisely the nil radical of \(\lambda\). A connection between a fuzzy semiprime ideal and the nil radical of a fuzzy ideal is thus obtained.