《交换代数》共分两卷，本书为其中的第二卷。该书由由哈佛大学著名数学家O.Zariski和法国数学家P.Samuel共同撰写，1958年由Nostrand出版公司出版，后来被译成俄、法等多种版本。1973年被纳Springer出版社的《数学研究生教材》第28、29卷。

经过时间验证，这套书的确是交换代数方面的经典教材。

这套两卷集教材由哈佛大学著名数学家O.Zariski和法国数学家P.Samuel共同撰写，1958年由Nostrand出版公司出版，后来被译成俄、法等多种版本。1973年被纳Springer出版社的《数学研究生教材》第28、29卷。经过时间验证，这套书的确是交换代数方面的经典教材。

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

CHPTER

 10. Dimension theory in power series rings

 11. Extension of the ground field

 12. Characteristic functions of graded modules and homogeneous ideals

 13. Chains of syzygies

VIII. LOCAL ALGEBRA

 1. The method of associated graded rings

 2. Some topological notions. Completions

 . Elementary properties of complete modules

 4. Zariski rings

 5. Comparison of topologies in a noetherian ring

 6. Finite extensions

 7. Hensel's lemma and applications

 8. Characteristic functions

 9. Dimension theory. Systems of parameters

 10. Theory of multiplicities

 11. Regular local rings

 12. Structure of complete local rings and applications

 13. Analytical irreducibility and analytical normality of normal varieties

APPENDIX

 1. Relations between prime ideals in a noetherian domain o and in a simple ring extension 0 It] of o.

 2. Valuations in noetherian domains

 3. Valuation ideals

 4. Complete modules and ideals

 5. Complete ideals in regular local rings of dimension 2

 6. Macaulay rings

 7. Unique factorization in regular local rings

INDEX OF DEFINITIONS