Commutative Algebra

With a View Toward Algebraic Geometry

Graduate Texts in Mathematics 150

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.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.
Rezension
D. Eisenbud Commutative Algebra with a View Toward Algebraic Geometry "This text has personality Those familiar with Eisenbud"s own research will recognize its traces in his choice of topics and manner of approach. The book conveys infectious enthusiasm and the conviction that research in the field is active and yet accessible." MATHEMATICAL REVIEWS
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Beschreibung

Produktdetails


Einband Taschenbuch
Seitenzahl 785
Erscheinungsdatum 11.02.1999
Serie Graduate Texts in Mathematics 150
Sprache Englisch
ISBN 978-3-540-94269-6
Verlag Springer
Maße (L/B/H) 238/156/48 mm
Gewicht 1216
Abbildungen XVI, w. mit 90 Illustrationen 23,5 cm
Auflage 1st ed. 1995. Corr. 3rd printing
Buch (Taschenbuch, Englisch)
42,75
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