(Mostly) Commutative Algebra

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.

“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)

• 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.-