CHAPTEE VI. VALUATION THEORY 1. Introductory remarks 2. Places 3. Specialization of places 4. Existence of places 5. The center of a place in a subring 5bis The notion of the center of a place in algebraic geometry 6. Places and field extensions 7. The case of an algebraic field extension 8. Valuations 9. Places and valuations 10. The rank of a valuation 11. Valuations and field extensions 12. Ramification theory of general valuations 13. Classical ideal theory and valuations 14. Prime divisors in fields of algebraic functions 15. Examples of valuations 16. An existence theorem for composite centered valuations 17. The abstract Riemann surface of a field 18. Derived normal models VII.POLYNOMIAL AND POWER SERIES RINGS 1.Formal power series 2.Graded rings and homogeneous ideals 3.Algebraic varieties in the affine 4.Algebraic varieties in the projective space 5.Relations betwwen non-homogeneous and homogeneous ideals 6.Relations betwwn affine and projective varieties 7.Dimentson theory in finte integral domaions 8.Special dimension-theoretic properties of polynomial rings 9.Normatlization theorems CHapter VIII.LOCAL ALGEBRA APPENDIX INDEX OF DEFINITIONS
