This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.Read more
- Gathers together all the major developments of the last 15 years
- Concise presentation of important computational methods
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'…an interesting collection of facts not easily found elsewhere.' Mathematika
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- Date Published: March 1994
- format: Paperback
- isbn: 9780521454841
- length: 340 pages
- dimensions: 229 x 152 x 18 mm
- weight: 0.483kg
- availability: Available
Table of Contents
1. Krull dimension
2. Syzygetic sequences
3. Approximation complexes
4. Linkage and Koszul homology
5. Arithmetic of Rees algebras
7. Ideal transforms
8. The equations of Rees algebras
9. Commuting varieties of algebras
10. Computational methods in commutative algebra.
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