Some properties of ideals in Cohen-Macaulay local rings
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910650920337408 |
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| author | Bartels, Richard F. |
| author_facet | Bartels, Richard F. |
| contents | For a Cohen-Macaulay local ring $(R,\mathfrak{m})$ with canonical module, we study how relations between $\text{index}(R)$ and $\text{g}\ell\ell(R)$ and between $\text{index}(R)$ and $e(R)$ are preserved when factoring out regular sequences and localizing at prime ideals. We then give conditions for when ideals in a one-dimensional Cohen-Macaulay local ring are Elias and Burch, and use these conditions to study the relationship between Elias, Burch, and Ulrich ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some properties of ideals in Cohen-Macaulay local rings Bartels, Richard F. Commutative Algebra For a Cohen-Macaulay local ring $(R,\mathfrak{m})$ with canonical module, we study how relations between $\text{index}(R)$ and $\text{g}\ell\ell(R)$ and between $\text{index}(R)$ and $e(R)$ are preserved when factoring out regular sequences and localizing at prime ideals. We then give conditions for when ideals in a one-dimensional Cohen-Macaulay local ring are Elias and Burch, and use these conditions to study the relationship between Elias, Burch, and Ulrich ideals. |
| title | Some properties of ideals in Cohen-Macaulay local rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2410.11144 |