This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry.

More than 300 exercises will allow the reader to deepen his understanding of the subject.

The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.

Informazioni sull?autore

Antoine Chambert-Loir (1971- ) is Professor of Mathematics at Universit� de Paris. He previously taught at the �cole normale sup�rieure, University Pierre-et-Marie-Curie, �cole polytechnique, University of Rennes and Universit� Paris-Sud. Besides coauthoring a 3-volume book of exercises in analysis, his books include A Field Guide to Algebra and, as co-author, the prize-winning Motivic Integration.

His current research is in arithmetic geometry.

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