1. Elementary lemmas from ideal theory

2. Primary decomposition in non-noetherian rings

3. Integral dependence

4. Linear algebra

5. Discriminant of an algebra

6. The discriminant ideal

7. Galois theory of local rings

8. Ordered abelian groups

9. Valuations

10. Specialization and composition of valuations

11. Ramification theory of valuations

12. Valuations of algebraic function fields

13. The dimension of a noetherian local ring

14. Quadratic transforms

15. Limits of quadratic sequences

16. Uniformization in a two-dimensional regular local domain

17. Uniformization for a two-dimensional algebraic function field

18. Projective varieties

19. Resolution of singularities of algebraic surfaces

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File created: 11/5/2009