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chambert-loir antoine - (mostly) commutative algebra

(Mostly) Commutative Algebra




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 04/2021
Edizione: 1st ed. 2021





Trama

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. 

 






Sommario

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.-






Autore

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.












Altre Informazioni

ISBN:

9783030615949

Condizione: Nuovo
Collana: Universitext
Dimensioni: 235 x 155 mm Ø 735 gr
Formato: Brossura
Illustration Notes:XV, 466 p. 18 illus., 6 illus. in color.
Pagine Arabe: 466
Pagine Romane: xv


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