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（巴黎與雷恩）為大學四年級學生開設的交換代數講義。在這個階段，學生已經修習過基礎線性代數課程，並且基本上熟悉域上向量空間的語言。本書介紹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，以及更進階主題的導論，例如同調代數、張量積，以及代數幾何中所涉及的代數概念。
全書包含超過 300 道習題，幫助讀者深化對本主題的理解。
本書亦收錄 11 篇歷史小品，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 年－）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冊的分析學習題書籍外，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（arithmetic geometry）。
