Integral closure of ideals
Douglas A. Leonard
TL;DR
This paper introduces a modified Qth-power algorithm and a non-homogeneous Rees algebra to compute integral closures of ideals in affine domains over finite fields, enhancing computational methods in algebraic geometry.
Contribution
It presents a novel modification of the Qth-power algorithm and introduces a non-homogeneous Rees algebra for better computation of integral closures of ideals.
Findings
Effective computation of integral closures using the modified algorithm.
Introduction of a non-homogeneous Rees algebra for ideal closures.
Enhanced structured presentations of integral closures in finite fields.
Abstract
The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite fields relative to a local monomial ordering. A non-homogeneous version of the standard (homogeneous) Rees algebra is introduced as well.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models