Integral closure of 1-dimensional rings
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915758219460608 |
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| author | Asgharzadeh, Mohsen |
| author_facet | Asgharzadeh, Mohsen |
| contents | We study certain properties of modules over 1-dimensional local integral domains. First, we examine the order of the conductor ideal and its expected relationship with multiplicity. Next, we investigate the reflexivity of certain colength-two ideals. Finally, we consider the freeness problem of the absolute integral closure of a DVR, and connect this to the reflexivity problem of $R^{\frac{1}{p^n}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integral closure of 1-dimensional rings Asgharzadeh, Mohsen Commutative Algebra We study certain properties of modules over 1-dimensional local integral domains. First, we examine the order of the conductor ideal and its expected relationship with multiplicity. Next, we investigate the reflexivity of certain colength-two ideals. Finally, we consider the freeness problem of the absolute integral closure of a DVR, and connect this to the reflexivity problem of $R^{\frac{1}{p^n}}$. |
| title | Integral closure of 1-dimensional rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2503.01640 |