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 graduatelevel 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 for the online version of the book.
Latest version posted in June 2012.
Click here for the 2006 electronic version of the book.
The chapter titles are:

What is integral closure of ideals?

Integral closure of rings

Separability

Noetherian rings

Rees algebras

Valuations

Derivations

Reductions

Analytically unramified rings

Rees valuations

Multiplicity and integral closure

The conductor

The BrianconSkoda Theorem

Twodimensional regular local rings

Computing integral closure

Integral dependence of modules

Joint reductions

Adjoints of ideals

Normal homomorphisms

Appendix A Some background material

Some forms of prime avoidance;
Caratheodory's theorem;
Grading;
Complexes;
Macaulay representation of numbers

Appendix B Height and dimension formulas

GoingDown, LyingOver, 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, updated all the time....
Last updated 9 December 2012.