论文标题
REES代数的某些二次标记的Hilbert-Kunz功能
The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
论文作者
论文摘要
鉴于$（R，\ Mathfrak m）$和理想的$ i $ r $ $ $ r $的换成本地戒指$（R，\ Mathfrak m），最近已经研究了REES代数$ r [IT] $的一家具，是Nagata的理想化和融合式的重复的一种统一方法，并作为构建有趣的例子，尤其是整体域。当$ r $是主要特征的noetherian时，我们会计算该家族成员的Hilbert-kunz功能，并且前提是$ i $是$ \ mathfrak {m} $ - primary或$ r $是常规的，f-finite，我们也会发现他们的希尔伯特 - 库恩兹多重性。探索了一些后果和示例。
Given a commutative local ring $(R,\mathfrak m)$ and an ideal $I$ of $R$, a family of quotients of the Rees algebra $R[It]$ 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 Hilbert-Kunz 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.
