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 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.