# Commutative Algebra

## with a View Toward Algebraic Geometry

Part of the Graduate Texts in Mathematics book series (GTM, volume 150)

Part of the Graduate Texts in Mathematics book series (GTM, volume 150)

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.

Algebraic Geometry algebra algebraic geometry category theory cohomology colimit commutative algebra Dimension field homological algebra linear algebra polynomial

- DOI https://doi.org/10.1007/978-1-4612-5350-1
- Copyright Information Springer-Verlag New York 1995
- Publisher Name Springer, New York, NY
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-78122-6
- Online ISBN 978-1-4612-5350-1
- Series Print ISSN 0072-5285
- About this book