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A course in commutative algebra

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概要 This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected... subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.--続きを見る
目次 Introduction
Part I. The Algebra-Geometry Lexicon. 1. Hilbertʹs Nullstellensatz
- 2. Noetherian and Artinian Rings
- 3. The Zariski Topology
- 4. A Summary of the Lexicon
Part II. Dimension. 5. Krull Dimension and Transcendence Degree
- 6. Localization
- 7. The Principal Ideal Theorem
- 8. Integral Extensions
Part III. Computational Methods. 9. Grobner Bases
- 10. Fibers and Images of Morphisms Revisited
- 11. Hilbert Series and Dimension
Part IV. Local Rings. 12. Dimension Theory
- 13. Regular Local Rings
- 14. Rings of Dimension One
Solutions of Some Exercises.
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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2011 English/International

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登録日 2020.06.27
更新日 2020.06.28