A singular introduction to commutative algebra
著者
書誌事項
A singular introduction to commutative algebra
Springer, c2002
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注記
Includes bibliographical references (p. [553]-562) and indexes
内容説明・目次
内容説明
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.
目次
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.
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