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.

Click here to link to the book information at Cambridge University Press.

Click here to link to the list of known errata.
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:
1. What is integral closure of ideals?
2. Integral closure of rings
3. Separability
4. Noetherian rings
5. Rees algebras
6. Valuations
7. Derivations
8. Reductions
9. Analytically unramified rings
10. Rees valuations
11. Multiplicity and integral closure
12. The conductor
13. The Briancon-Skoda Theorem
14. Two-dimensional regular local rings
15. Computing integral closure
16. Integral dependence of modules
17. Joint reductions
18. Adjoints of ideals
19. 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
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, updated all the time.... Last updated 9 December 2012.