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.

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