Analysis reveals when fitting ideals equal the original ideal in a Noetherian ring, indicating properties of local rings.
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.
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Eisenbud et al. (2025) studied this question.
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