On generalized Narita ideals
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912199390265344 |
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| author | Puthenpurakal, Tony J. |
| author_facet | Puthenpurakal, Tony J. |
| contents | Let $(A,\mathfrak{m})$ be a Cohen-Macaulay local ring of dimension $d \geq 2$. An $\mathfrak{m}$-primary ideal $I$ is said to be a generalized Narita ideal if $e_i^I(A) = 0$ for $2 \leq i \leq d$. If $I$ is a generalized Narita ideal and $M$ is a maximal Cohen-Macaulay $A$-module then we show $e_i^I(M) = 0$ for $2 \leq i \leq d$. We also have $G_I(M)$ is generalized Cohen-Macaulay. Furthermore we show that there exists $c_I$ (depending only on $A$ and $I$) such that $\text{reg} \ G_I(M) \leq c_I$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12819 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On generalized Narita ideals Puthenpurakal, Tony J. Commutative Algebra Primary 13A30, Secondary 13D40, 13D07, 13D45 Let $(A,\mathfrak{m})$ be a Cohen-Macaulay local ring of dimension $d \geq 2$. An $\mathfrak{m}$-primary ideal $I$ is said to be a generalized Narita ideal if $e_i^I(A) = 0$ for $2 \leq i \leq d$. If $I$ is a generalized Narita ideal and $M$ is a maximal Cohen-Macaulay $A$-module then we show $e_i^I(M) = 0$ for $2 \leq i \leq d$. We also have $G_I(M)$ is generalized Cohen-Macaulay. Furthermore we show that there exists $c_I$ (depending only on $A$ and $I$) such that $\text{reg} \ G_I(M) \leq c_I$. |
| title | On generalized Narita ideals |
| topic | Commutative Algebra Primary 13A30, Secondary 13D40, 13D07, 13D45 |
| url | https://arxiv.org/abs/2501.12819 |