Syzygies [Paperback]

This 1985 book covers from first principles the theory of Syzygies.The aim of this book, which was originally published in 1985, is to cover from first principles the theory of Syzygies, building up from a discussion of the basic commutative algebra to such results as the authors proof of the Syzygy Theorem.The aim of this book, which was originally published in 1985, is to cover from first principles the theory of Syzygies, building up from a discussion of the basic commutative algebra to such results as the authors proof of the Syzygy Theorem.The aim of this book, which was originally published in 1985, is to cover from first principles the theory of Syzygies, building up from a discussion of the basic commutative algebra to such results as the authors' proof of the Syzygy Theorem. In the last three chapters applications of the theory to commutative algebra and algebraic geometry are given.0. Foundations; 1. Counting depths; 2. Basic element theory; 3. Fundamental theorems on stzygies; 4. Selected applications; 5. Filtrations on modules based on chomology; 6. Vector bundles on the punctured spectrum of a regular local ring; Appendix; References; Index.