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＜電子ブック＞
(Mostly) Commutative Algebra / by Antoine Chambert-Loir
(Universitext. ISSN:21916675)

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
本文言語	英語
大きさ	XV, 466 p. 18 illus., 6 illus. in color : online resource
著者標目	*Chambert-Loir, Antoine author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic fields LCSH:Polynomials LCSH:Algebras, Linear LCSH:Algebra, Homological LCSH:Algebraic geometry FREE:Algebra FREE:Commutative Rings and Algebras FREE:Field Theory and Polynomials FREE:Linear Algebra FREE:Category Theory, Homological Algebra FREE:Algebraic Geometry
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-030-61595-6

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