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.
Les mer
with a View Toward Algebraic Geometry
Produktdetaljer
ISBN
9781461253501
Publisert
2020
Utgiver
Vendor
Springer
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter