A simple proof of some generalized principal ideal theorems

DOI10.1090/S0002-9939-01-05877-4zbMath0979.13008arXivmath/0209186MaRDI QIDQ2716094

David Eisenbud, Bernd Ulrich, Craig Huneke

Publication date: 6 June 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0209186

zbMATH Keywords

determinantal idealsheightsymmetric algebrasorder idealFitting idealsgeneralized principal ideal theoremequidimensionalityrank of finitely generated module

Mathematics Subject Classification ID

Linkage, complete intersections and determinantal ideals (13C40) Commutative Noetherian rings and modules (13E05) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Deformations and infinitesimal methods in commutative ring theory (13D10)

Related Items (5)

Codimension and connectedness of degeneracy loci over local rings ⋮ Multiplicities for arbitrary modules and reduction ⋮ BLOWUPS AND FIBERS OF MORPHISMS ⋮ A study of singularities on rational curves via syzygies ⋮ Row ideals of certain normal ideals

Cites Work

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• Order ideals and a generalized Krull height theorem
• The dimension and components of symmetric algebras
• Bounds for codimensions of Fitting ideals
• Algèbre locale. Multiplicités. Cours au Collège de France, 1957-1958, rédigé par Pierre Gabriel. 2e ed.
• The Eisenbud-Evans Generalized Principal Ideal Theorem and Determinantal Ideals
• Heights of ideals of minors
• Equidimensional symmetric algebras and residual intersections
• A generalized principal ideal theorem

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