The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
Given a commutative local ring $(R, \mathfrak{m})$ and an ideal $I$ of $R$, a family of quotients of the Rees algebra $R[I t]$ has been recently studied as a unified approach to the Nagata's idealization and the amalgamated duplication and as a way to construct interesting examples, especially integ...
| Autores: | ; |
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| Tipo de documento: | Artigo |
| Estado: | Accepted version |
| Data de publicação: | 2022 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/193549 |
| Acesso em linha: | https://hdl.handle.net/2445/193549 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Anells locals Àlgebra commutativa Àlgebra homològica Local rings Commutative algebra Homological algebra |
| Resumo: | Given a commutative local ring $(R, \mathfrak{m})$ and an ideal $I$ of $R$, a family of quotients of the Rees algebra $R[I t]$ has been recently studied as a unified approach to the Nagata's idealization and the amalgamated duplication and as a way to construct interesting examples, especially integral domains. When $R$ is noetherian of prime characteristic, we compute the HilbertKunz function of the members of this family and, provided that either $I$ is $\mathfrak{m}$-primary or $R$ is regular and F-finite, we also find their Hilbert-Kunz multiplicity. Some consequences and examples are explored. |
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