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(Mostly) Commutative Algebra

(Mostly) Commutative Algebra

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Wydawnictwo Springer Nature Customer Service Center GmbH
Data wydania 01/04/2021
Wydanie Pierwsze
Liczba stron 466
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla szkół wyższych i kształcenia podyplomowego
Język angielski
ISBN 9783030615949
Kategorie Podstawy matematyki, Algebra, Geometria algebraiczna
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Opis książki

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.

(Mostly) Commutative Algebra

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.-

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