國立虎尾科技大學 |

(Mostly) Commutative Algebra

Record Type:	Language materials, printed : Monograph/item
Title/Author:	(Mostly) Commutative Algebra/ by Antoine Chambert-Loir.
Author:	Chambert-Loir, Antoine.
Description:	XV, 466 p. 18 illus., 6 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Algebra. -
Online resource:	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. - 1st ed. 2021. - XV, 466 p. 18 illus., 6 illus. in color.online resource. - 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:

579870
Algebra.

LC Class. No.: QA150-272

Dewey Class. No.: 512

(Mostly) Commutative Algebra
LDR:02509nam a22003975i 4500 001 1050476
003 DE-He213
005 20210916073455.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030615956 $9 978-3-030-61595-6
024 7 $a 10.1007/978-3-030-61595-6 $2 doi
035 $a 978-3-030-61595-6
050 4 $a QA150-272
072 7 $a PBF $2 bicssc
072 7 $a MAT002000 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512 $2 23
100 1 $a Chambert-Loir, Antoine. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 676688
245 1 0 $a (Mostly) Commutative Algebra $h [electronic resource] / $c by Antoine Chambert-Loir.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XV, 466 p. 18 illus., 6 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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.
650 0 $a Algebra. $2 gtt $3 579870
650 0 $a Commutative algebra. $3 672047
650 0 $a Commutative rings. $3 672474
650 0 $a Field theory (Physics). $3 685987
650 0 $a Algebras, Linear. $3 528115
650 0 $a Category theory (Mathematics). $3 1255325
650 0 $a Homological algebra. $3 1255326
650 0 $a Algebraic geometry. $3 1255324
650 2 4 $a Commutative Rings and Algebras. $3 672054
650 2 4 $a Field Theory and Polynomials. $3 672025
650 2 4 $a Linear Algebra. $3 1207620
650 2 4 $a Category Theory, Homological Algebra. $3 678397
650 2 4 $a Algebraic Geometry. $3 670184
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030615949
776 0 8 $i Printed edition: $z 9783030615963
830 0 $a Universitext, $x 0172-5939 $3 1253835
856 4 0 $u https://doi.org/10.1007/978-3-030-61595-6
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)