相關主題
商品描述
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.
商品描述(中文翻譯)
本書源自於法國兩所大學（Paris 和 Rennes）為大學四年級學生所開設的交換代數（commutative algebra）講義。在這個階段，學生已修習過基礎線性代數課程，並且基本熟悉域上向量空間的相關語言。本書涵蓋的主題包括環的算術、模組（尤其是主理想環，以及此類環上模組的分類）、Galois 理論，以及進階主題的介紹，例如同調代數（homological algebra）、張量積（tensor product），還有代數幾何中所涉及的代數概念。
超過 300 道習題將幫助讀者深化對本主題的理解。
本書還收錄了 11 篇歷史小札，介紹對交換代數有所貢獻的數學家。
作者簡介
Antoine Chambert-Loir (1971- ) is Professor of Mathematics at Université de Paris. He previously taught at the École normale supérieure, University Pierre-et-Marie-Curie, École polytechnique, University of Rennes and Université 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.
作者簡介(中文翻譯)
Antoine Chambert-Loir（1971－）是 Université de Paris 的數學教授。他曾任教於 École normale supérieure、University Pierre-et-Marie-Curie、École polytechnique、University of Rennes 以及 Université Paris-Sud。除了與他人合著一套三卷本的分析學習題書籍之外，他的著作還包括《A Field Guide to Algebra》，以及與他人合著、曾獲獎的《Motivic Integration》。
他目前的研究領域是算術幾何。
