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(Mostly) commutative algebra

Chambert-Loir, Antoine.

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(Mostly) commutative algebra

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	(Mostly) commutative algebra/ by 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.
內容註:	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.
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

(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

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

604140
Commutative algebra.

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

Dewey Class. No.: 512.44

(Mostly) commutative algebra
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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 516203
650 2 4 $a Commutative Rings and Algebras. $3 891076
650 2 4 $a Field Theory and Polynomials. $3 891077
650 2 4 $a Linear Algebra. $3 3338825
650 2 4 $a Category Theory, Homological Algebra. $3 899944
650 2 4 $a Algebraic Geometry. $3 893861
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