Abstract For an ideal I in a Noetherian ring R, the Fitting ideals Fittⱼ (I) are studied. We discuss the question of when Fittⱼ (I) =I or Fittⱼ (I) =I for some j. A classical case is the Hilbert–Burch theorem when j=1 and I is a perfect ideal of grade 2 in a local ring.
Eisenbud et al. (Wed,) studied this question.