On the Stability of Bass and Betti Numbers under Ideal Perturbations in a Local Ring
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909712143876096 |
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| author | Trung, Van Duc |
| author_facet | Trung, Van Duc |
| contents | Let $(R,\mathfrak{m})$ be a Noetherian local ring, and let $J$ be an arbitrary ideal of $R$. Suppose $M$ is a finitely generated $R$-module. Let $x_1,\ldots,x_r$ be a $J$-filter regular sequence on $M$. We provide an explicit number $N$ such that the Bass and Betti numbers of $M/(x_1, \ldots, x_r)M$ are preserved when we perturb the sequence $x_1, \ldots,x_r$ by $\varepsilon_1, \ldots, \varepsilon_r \in \mathfrak{m}^N$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_22364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Stability of Bass and Betti Numbers under Ideal Perturbations in a Local Ring Trung, Van Duc Commutative Algebra 13D07, 13D10 F.2.2; I.2.7 Let $(R,\mathfrak{m})$ be a Noetherian local ring, and let $J$ be an arbitrary ideal of $R$. Suppose $M$ is a finitely generated $R$-module. Let $x_1,\ldots,x_r$ be a $J$-filter regular sequence on $M$. We provide an explicit number $N$ such that the Bass and Betti numbers of $M/(x_1, \ldots, x_r)M$ are preserved when we perturb the sequence $x_1, \ldots,x_r$ by $\varepsilon_1, \ldots, \varepsilon_r \in \mathfrak{m}^N$. |
| title | On the Stability of Bass and Betti Numbers under Ideal Perturbations in a Local Ring |
| topic | Commutative Algebra 13D07, 13D10 F.2.2; I.2.7 |
| url | https://arxiv.org/abs/2507.22364 |