2020/02/01 by Francesco Strazzanti, Strazzanti, Francesco, Santiago Zarzuela Armengou +1
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC
paper · pdf · doi:10.48550/arxiv.2002.00282
To appear in the Proceedings of the American Mathematical Society
openalex publication_date 2020/02/01 · arxiv created 2021/09/05 · arxiv updated 2021/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \mathfrakm-primary or R is regular and F-finite, we also find their Hilbert-Kunz multiplicity. Some consequences and examples are explored.