Ideals and their Fitting ideals
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912632775114752 |
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| author | Eisenbud, David Ficarra, Antonino Herzog, Jürgen Moradi, Somayeh |
| author_facet | Eisenbud, David Ficarra, Antonino Herzog, Jürgen Moradi, Somayeh |
| contents | For an ideal $I$ in a Noetherian ring $R$, the Fitting ideals $\textrm{Fitt}_j(I)$ are studied. We discuss the question of when $\textrm{Fitt}_j(I)=I$ or $\sqrt{\textrm{Fitt}_j(I)}=\sqrt{I}$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_00541 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ideals and their Fitting ideals Eisenbud, David Ficarra, Antonino Herzog, Jürgen Moradi, Somayeh Commutative Algebra 13C05, 05E40 For an ideal $I$ in a Noetherian ring $R$, the Fitting ideals $\textrm{Fitt}_j(I)$ are studied. We discuss the question of when $\textrm{Fitt}_j(I)=I$ or $\sqrt{\textrm{Fitt}_j(I)}=\sqrt{I}$ 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. |
| title | Ideals and their Fitting ideals |
| topic | Commutative Algebra 13C05, 05E40 |
| url | https://arxiv.org/abs/2401.00541 |