Integral closure of ideals

2012/09/18 by Douglas A. Leonard, Leonard, Douglas A. · 7 citations
Computer Science · Mathematics · #Polynomial and algebraic computation #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1209.4070

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.

Cited by

• Decomposition of integrally closed ideals in Arf rings
• Stable trace ideals and applications
• The Diophantine problem in finitely generated commutative rings
• Stanley depth of the integral closure of monomial ideals
• The Recursion Formula for Mixed Multiplicities with respect to Joint\n Reductions
• Maximal Cohen-Macaulay modules that are not locally free on the punctured spectrum
• Stability of Associated Primes and Depth of Integral Closures of Powers of Edge Ideals
• Grothendieck groups, convex cones and maximal Cohen-Macaulay points

Related

• The Qth-power algorithm in characteristic 0
• Specialization of Integral Closure of Ideals by General Elements
• Integral closures of monomial ideals and Fulkersonian hypergraphs
• New versions of Frobenius and integral closure of ideals
• Rees algebras on smooth schemes: integral closure and higher differential operators