Upper bound of multiplicity in Cohen-Macaulay rings of prime characteristic
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913685940731904 |
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| author | Huong, Duong Thi Quy, Pham Hung |
| author_facet | Huong, Duong Thi Quy, Pham Hung |
| contents | Let $(R, \frak m)$ be a local ring of prime characteristic $p$ and of dimension $d$ with the embedding dimension $v$, type $s$ and the Frobenius test exponent for parameter ideals $\mathrm{Fte}(R)$. We will give an upper bound for the multiplicity of Cohen-Macaulay rings in prime characteristic in terms of $\mathrm{Fte}(R),d,v$ and $s$. Our result extends the main results for Gorenstein rings due to Huneke and Watanabe. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper bound of multiplicity in Cohen-Macaulay rings of prime characteristic Huong, Duong Thi Quy, Pham Hung Commutative Algebra 13A35, 13H10 Let $(R, \frak m)$ be a local ring of prime characteristic $p$ and of dimension $d$ with the embedding dimension $v$, type $s$ and the Frobenius test exponent for parameter ideals $\mathrm{Fte}(R)$. We will give an upper bound for the multiplicity of Cohen-Macaulay rings in prime characteristic in terms of $\mathrm{Fte}(R),d,v$ and $s$. Our result extends the main results for Gorenstein rings due to Huneke and Watanabe. |
| title | Upper bound of multiplicity in Cohen-Macaulay rings of prime characteristic |
| topic | Commutative Algebra 13A35, 13H10 |
| url | https://arxiv.org/abs/2502.06880 |