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: |
Table of 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.