Commutative Algebra: with a View Toward Algebraic Geometry

Graduate Texts in Mathematics #150

by David Eisenbud

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.

Genres: Mathematics, Algebra, Textbooks, Science, Geometry

816 pages, Paperback

First published March 30, 1995

Reviews

[Geoffrey Lee · Rating 3 out of 5]

This book seems to be highly non-self contained, by that I mean it seems to assume a prior knowledge of some basic Algebra. There are way too many typos in it and many of them in homework problems >.<

[Mike · Rating 5 out of 5]

Commutative algebra has been very rightly considered the most-difficult general field of math and thus is one that is in especial need of good texts for the advanced student. By "good", such a text needs to both be written in clear prose and able to address its topics head-on, but also must be able to inter-relate its topics to other issues in maths that could be germane to further inquiry on the part of the reader. This text meets all the above goals in a masterful manner.

[D.]

Commutative algebra with a view toward algebraic geometry by David. Eisenbud (1995)