A course in commutative algebra
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...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Berlin, Heidelberg
Springer
2011
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| Schriftenreihe: | Graduate texts in mathematics
256 |
| Schlagworte: | |
| Online Zugang: | Inhaltstext Einführung/Vorwort Cover Inhaltsverzeichnis |
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| Zusammenfassung: | 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. 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.-- |
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| Beschreibung: | Literaturverzeichnis: Seiten 235-237 |
| Beschreibung: | xi, 246 Seiten Diagramme |
| ISBN: | 9783642035449 978-3-642-03544-9 |