Hilbert-Kunz Multiplicity of Fiber Product Rings and Nagata Idealizations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909753965281280 |
|---|---|
| author | Jorge-Pérez, Victor H. Martins, Paulo D. C. Lima, J. A. |
| author_facet | Jorge-Pérez, Victor H. Martins, Paulo D. C. Lima, J. A. |
| contents | The main purpose of this paper is to provide formulas for the Hilbert-Kunz multiplicity of fiber product rings and Nagata idealizations. We give explicit formulas for the Hilbert-Kunz multiplicity of a fiber product $R \times_T S$, where $R$, $S$, and $T$ are Noetherian local rings sharing the same characteristic and residue field. We compute the Hilbert-Kunz multiplicity of a general Nagata idealization $R \ltimes M$, where $M$ is a finitely generated $R$-module. Additionally, we provide examples, structural results and establish new bounds for the Hilbert-Kunz multiplicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hilbert-Kunz Multiplicity of Fiber Product Rings and Nagata Idealizations Jorge-Pérez, Victor H. Martins, Paulo D. C. Lima, J. A. Commutative Algebra 13D40, 13H15, 13H05 The main purpose of this paper is to provide formulas for the Hilbert-Kunz multiplicity of fiber product rings and Nagata idealizations. We give explicit formulas for the Hilbert-Kunz multiplicity of a fiber product $R \times_T S$, where $R$, $S$, and $T$ are Noetherian local rings sharing the same characteristic and residue field. We compute the Hilbert-Kunz multiplicity of a general Nagata idealization $R \ltimes M$, where $M$ is a finitely generated $R$-module. Additionally, we provide examples, structural results and establish new bounds for the Hilbert-Kunz multiplicity. |
| title | Hilbert-Kunz Multiplicity of Fiber Product Rings and Nagata Idealizations |
| topic | Commutative Algebra 13D40, 13H15, 13H05 |
| url | https://arxiv.org/abs/2405.15075 |