Ideals and their Fitting ideals

2023/12/31 by David Eisenbud, Antonino Ficarra, Eisenbud, David +5 · 1 citation
Computer Science · Mathematics · #05E40 #13C05 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2401.00541

openalex publication_date 2023/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an ideal I in a Noetherian ring R, the Fitting ideals \textrmFitt_j(I) are studied. We discuss the question of when \textrmFitt_j(I)=I or √\textrmFitt_j(I)=√(I) for some j. A classical case is the Hilbert-Burch theorem when j=1 and I is a perfect ideal of grade 2 in a local ring.

Cited by

• On strong Euler-homogeneity and Saito-holonomicity for complex hypersurfaces

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