Description
(Text)
This book can be understood as a model for teaching commutative algebra, taking into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, it is shown how to handle it by computer. The computations are exemplified with the computer algebra system SINGULAR developed by the authors. SINGULAR is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD with a version of SINGULAR for various platforms (Unix/Linux, Windows, Macintosh), including all examples and procedures explained in the book. The book can be used for courses, seminars and as a basis for studying research papers in commutative algebra, computer algebra and algebraic geometry.
(Table of content)
From the contents:
- 1 Rings, Ideals and Standard Bases
- 2. Modules
- 3. Noether Normalization and Applications
- 4. Primary Decomposition and Related Topics
- 5. Hilbert Function
- 6. Complete Local Rings
- 7. Homological Algebra
- Appendix A. Geometric Background
- Appendix B. SINGULAR - A Short Introduction
- B. SINGULAR Reference Manual
- Index
- Glossary
