Strazzanti, FrancescoZarzuela, Santiago2023-02-132023-02-132022-040002-9939https://hdl.handle.net/2445/193549Given 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.11 p.application/pdfengcc-by-nc-nd (c) American Mathematical Society (AMS), 2022https://creativecommons.org/licenses/by-nc-nd/4.0/Anells localsÀlgebra commutativaÀlgebra homològicaLocal ringsCommutative algebraHomological algebrainfo:eu-repo/semantics/article7139092023-02-13info:eu-repo/semantics/openAccess