Fuzzy semiprimary ideals of rings

Abstract The concept of fuzzy ideals is extended by introducing fuzzy semiprimary ideals in rings. This class of fuzzy ideals generalizes the class of fuzzy semiprimary ideals. It is shown that there do exist fuzzy ideals which are fuzzy semiprimary but not fuzzy primary. A study of (i) the level ideals of a fuzzy semiprimary ideal (ii) the characteristic function of a semiprimary ideal (iii) the zero divisors in the ring of all fuzzy cosets of a fuzzy semiprimary ideal and (iv) the algebraic nature of direct and inverse images of fuzzy semiprimary ideals under homomorphisms is carried out.