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Commutative Algebra - with a View Toward Algebraic Geometry (Hardcover)
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Commutative Algebra - with a View Toward Algebraic Geometry (Hardcover)
Series: Graduate Texts in Mathematics, 150
Expected to ship within 9 - 17 working days
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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.
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