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.
The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
Francesco Strazzanti
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2022-01-01
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.
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