On semiprime fuzzy ideals (Q1319443)

The authors define the concept of a semiprime fuzzy ideal of a ring \(R\) in a different manner than has been done previously. Their definition is equivalent to previous definitions and makes use of the grade of membership of an element of \(R\). The authors then determine some basic properties of semiprime fuzzy ideals. Let \(f\) be a homomorphism of \(R\) onto a ring \(R'\), \(S'\) a semiprime fuzzy ideal of \(R'\), and \(S\) a semiprime fuzzy ideal of \(R\). The authors show that \(f^{-1}(S')\) is a semiprime fuzzy ideal of \(R\) and if \(f\) is constant on its kernel, then \(f(S)\) is a semiprime ideal of \(R'\). The authors also show that a fuzzy ideal is semiprime if and only if it is the intersection of all prime fuzzy ideals which contain it.