English

Ideals and their Fitting ideals

Commutative Algebra 2025-10-08 v1

Abstract

For an ideal II in a Noetherian ring RR, the Fitting ideals Fittj(I)\textrm{Fitt}_j(I) are studied. We discuss the question of when Fittj(I)=I\textrm{Fitt}_j(I)=I or Fittj(I)=I\sqrt{\textrm{Fitt}_j(I)}=\sqrt{I} for some jj. A classical case is the Hilbert-Burch theorem when j=1j=1 and II is a perfect ideal of grade 22 in a local ring.

Keywords

Cite

@article{arxiv.2401.00541,
  title  = {Ideals and their Fitting ideals},
  author = {David Eisenbud and Antonino Ficarra and Jürgen Herzog and Somayeh Moradi},
  journal= {arXiv preprint arXiv:2401.00541},
  year   = {2025}
}
R2 v1 2026-06-28T14:05:38.976Z