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(Mostly) commutative algebra

Chambert-Loir, Antoine.

(Mostly) commutative algebra

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	(Mostly) commutative algebraby Antoine Chambert-Loir.
作者:	Chambert-Loir, Antoine.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xv, 466 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Commutative algebra.
電子資源:	https://doi.org/10.1007/978-3-030-61595-6
ISBN:	9783030615956$q(electronic bk.)

(Mostly) commutative algebra
Chambert-Loir, Antoine.

(Mostly) commutative algebra[electronic resource] /by Antoine Chambert-Loir. - Cham :Springer International Publishing :2021. - xv, 466 p. :ill., digital ;24 cm. - Universitext,2191-6675. - Universitext..

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.

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.

ISBN: 9783030615956$q(electronic bk.)

Standard No.: 10.1007/978-3-030-61595-6doiSubjects--Topical Terms:

190842
Commutative algebra.

LC Class. No.: QA251.3 / .C43 2021

Dewey Class. No.: 512.44

(Mostly) commutative algebra
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245 1 0 $a (Mostly) commutative algebra $h [electronic resource] / $c by Antoine Chambert-Loir.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xv, 466 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 2191-6675
505 0 $a 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.
520 $a 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.
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650 1 4 $a Algebra. $3 188312
650 2 4 $a Commutative Rings and Algebras. $3 274057
650 2 4 $a Field Theory and Polynomials. $3 274058
650 2 4 $a Linear Algebra. $3 821215
650 2 4 $a Category Theory, Homological Algebra. $3 275954
650 2 4 $a Algebraic Geometry. $3 274807
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