A Singular Introduction to Commutative Algebra
Edition: 1 edition
Publisher: Springer
Published: October 3, 2002
Language: eng
Format: Paperback
Number of pages: 588
ISBN-13: 9783540428978
Subjects: Groups & group theory; Mathematical theory of computation; Algebra - General; Algebra; Mathematics; Science/Mathematics; Commutative algebra; Group Theory; Mathematics / Algebra / General; algebraic geometry; computer algebra
First sentence: The concept of a ring is probably the most basic one in commutative and non-commutative algebra.
Description: 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 text starts with the theory of rings and modules and standard bases with emphasis on local rings and localization. It is followed by the central concepts of commutative algebra such as integral closure, dimension theory, primary decomposition, Hilbert function, completion, flatness and homological algebra. There is a substantial appendix about algebraic geometry in order to explain how commutative algebra and computer algebra can be used for a better understanding of geometric problems. The book includes a CD with a distribution 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.