A course in commutative algebra
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 mainta...
| Main Author: | Kemper, Gregor, 1963- |
|---|---|
| Other Authors: | SpringerLink (Online service) |
| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht ; New York :
Springer,
©2011.
Dordrecht ; New York : [2011] |
| Physical Description: |
1 online resource (xi, 246 pages) : illustrations. |
| Series: |
Graduate texts in mathematics ;
256. |
| Subjects: |
| 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.-- |
|---|---|
| Item Description: |
Includes bibliographical references (pages 235-237) and indexes. 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.-- Back cover. English. |
| Physical Description: |
1 online resource (xi, 246 pages) : illustrations. |
| Bibliography: |
Includes bibliographical references (pages 235-237) and indexes. |
| ISBN: |
9783642035456 3642035450 |