Specialization and Integral Closure

2006/11/25 by Jooyoun Hong, Benjamin J. Ulrich, Hong, J. +1 · 1 citation
Computer Science · Mathematics · #13B22 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/0611773

openalex publication_date 2006/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the integral closedness of any ideal of height at least two is compatible with specialization by a generic element. This opens the possibility for proofs using induction on the height of an ideal. Also, with additional assumptions, we show that an element is integral over a module if it is integral modulo a generic element of the module. This turns questions about integral closures of modules into problems about integral closures of ideals, by means of a construction known as Bourbaki ideal.

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• Rational symbolic powers of ideals

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