The Hilbert-Kunz function of some quadratic quotients of the Rees algebra. (English) Zbl 1480.13015
Authors’ abstract: Given a commutative local ring \((R, m)\) 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 \(m\)-primary or \(R\) is regular and \(F\)-finite, we also find their Hilbert-Kunz multiplicity. Some consequences and examples are explored.
Reviewer: Amir Mafi (Sanandaj and Tehran)
MSC:
| 13D40 | Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series |
| 13H15 | Multiplicity theory and related topics |
| 13A30 | Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics |
Keywords:
Hilbert-Kunz functionReferences:
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