A family of quotients of the Rees algebra

2014/03/17 by Valentina Barucci, Barucci, Valentina, Marco D’Anna +4 · 1 citation
Mathematics · #13A30 #13H10 #20M14 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13A30 #msc:13H10 #msc:20M14

paper · pdf · doi:10.48550/arxiv.1403.4200

17 pages. To appear on "Communications in Algebra"

arxiv created 2014/03/17 · openalex publication_date 2014/03/17 · arxiv updated 2014/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A family of quotient rings of the Rees algebra associated to a commutative ring is studied. This family generalizes both the classical concept of idealization by Nagata and a more recent concept, the amalgamated duplication of a ring. It is shown that several properties of the rings of this family do not depend on the particular member.

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• A characterization of the Arf property for quadratic quotients of the Rees algebra

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