| Description |
1 online resource (xi, 246 pages) : illustrations |
| Series |
Graduate texts in mathematics ; 256 |
|
Graduate texts in mathematics ; 256.
|
| Contents |
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 |
| Summary |
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.-- Back cover |
| Bibliography |
Includes bibliographical references (pages 235-237) and indexes |
| Notes |
English |
|
Print version record |
| In |
Springer eBooks |
| Subject |
Commutative algebra.
|
|
Álgebra conmutativa
|
|
Commutative algebra
|
|
Kommutative Algebra
|
| Form |
Electronic book
|
| LC no. |
2013444043 |
| ISBN |
9783642035456 |
|
3642035450 |
|
