On fuzzy irreducible ideals and homomorphisms (Q1311776)

In [ibid. 42, 369-379 (1991; Zbl 0745.16002), Theorem 4.4], we showed the following: If \(f\) is a homomorphism from a ring \(R\) onto a Boolean ring \(R'\) then the mapping \(\theta \to f(\theta)\) defines a one-to-one correspondence between the set of all \(f\)-invariant fuzzy irreducible ideals of \(R\) and the set of all fuzzy irreducible ideals of \(R'\). In this note, we show that the condition: the ring \(R'\) is Boolean can be replaced by each fuzzy ideal of \(R\) is \(f\)-invariant.