Integral Closure of Ideals, Rings, and Modules
Integral Closure of Ideals, Rings, and Modules
by Irena Swanson and Craig Huneke
Integral Closure of Ideals, Rings, and Modules,
with
Craig Huneke,
published by
Cambridge University Press, Cambridge, 2006.
This is a graduate-level textbook,
and it is also meant to be a reference for researchers.
We assume some basic background in commutative algebra,
such as completions.
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Click here to link to the list of known errata.
Click here for the online version of the book.
Latest version posted in February 2023.
Click here for the 2006 electronic version of the book.
The chapter titles are:
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What is integral closure of ideals?
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Integral closure of rings
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Separability
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Noetherian rings
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Rees algebras
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Valuations
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Derivations
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Reductions
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Analytically unramified rings
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Rees valuations
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Multiplicity and integral closure
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The conductor
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The Briancon-Skoda Theorem
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Two-dimensional regular local rings
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Computing integral closure
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Integral dependence of modules
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Joint reductions
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Adjoints of ideals
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Normal homomorphisms
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Appendix A Some background material
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Some forms of prime avoidance;
Caratheodory's theorem;
Grading;
Complexes;
Macaulay representation of numbers
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Appendix B Height and dimension formulas
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Going-Down, Lying-Over, flatness;
Dimension and height inequalities;
Dimension formula;
Formal equidimensionality;
Dimension Formula
How to cite the book:
C. Huneke and I. Swanson,
{\it Integral Closure of Ideals, Rings, and Modules},
London Mathematical Society Lecture Note Series, 336.
Cambridge University Press, Cambridge, 2006.
Created: 11 October 2006.
Created at Purdue: 2 July 2020. Last updated 2 August 2023.