(Mostly) Commutative Algebra

ISBN-13: 9783030615949 / Angielski / Miękka / 2021 / 466 str.

Antoine Chambert-Loir

Recenzje

"This book on commutative algebra is more accessible for undergraduate student than the classical introductory books on this topic. ... The author has made a special effort in explaining carefully the definitions and presenting many clarifying examples. ... Each chapter ends with a large selection of exercises of different levels. ... This book is a gentle introduction ... that it will very useful for students and teachers in this area. Moreover, it suggests several new directions for deeper study." (Blas Torrecillas, zbMATH 1477.13001, 2022)

Spis treści

Preface.- 1 Rings.- 2 Ideals and divisibility.- 3 Modules.- 4 Field extensions.- 5 Modules over principal ideal rings.- 6 Noetherian and artinian rings. Primary decomposition.- 7 First steps in homological algebra.- 8 Tensor products and determinants.- 9 Commutative algebra: the normalization theorem, dimension theory, Dedekind rings.- Appendix.- References.- Index.-

O autorze

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.

Blurb

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.