東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

FindBook

Google Book

Amazon

博客來

From rings and modules to Hopf algebras = one flew over the algebraist's nest /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	From rings and modules to Hopf algebras/ by Michel Broue.
其他題名:	one flew over the algebraist's nest /
作者:	Broue, Michel.
出版者:	Cham :Springer International Publishing : : 2024.,
面頁冊數:	x, 533 p. :ill. (some col.), digital ;24 cm.
內容註:	1 Prerequisites and Preliminaries -- Part I Rings and Modules -- 2 Rings, Polynomials, Divisibility -- 3 Polynomial Rings in Several Indeterminates -- 4 More on Modules -- 5 On Representations of Finite Groups -- Part II Integral Domains, Polynomials, Fields -- 6 Prime and Maximal Ideals, Integral Domains -- 7 Fields, Division Rings -- Part III Finitely Generated Modules -- 8 Integrality, Noetherianity -- 9 Finitely Generated Projective Modules -- 10 Finitely Generated Modules Over Dedekind Domains -- 11 Complement on Dedekind Domains -- Part IV Characteristic Zero Linear Representations of Finite Groups -- 12 Monoidal Categories: An Introduction -- 13 Characteristic 0 Representations -- 14 Playing With the Base Field -- 15 Induction and Restriction: Some Applications to Finite Groups -- 16 Brauer's Theorem and Some Applications -- 17 Graded Representations and Characters -- 18 The Drinfeld-Lusztig Double of a Group Algebra.
Contained By:	Springer Nature eBook
標題:	Algebra. -
電子資源:	https://doi.org/10.1007/978-3-031-50062-6
ISBN:	9783031500626

From rings and modules to Hopf algebras = one flew over the algebraist's nest /
Broue, Michel.

From rings and modules to Hopf algebrasone flew over the algebraist's nest /[electronic resource] :by Michel Broue. - Cham :Springer International Publishing :2024. - x, 533 p. :ill. (some col.), digital ;24 cm.

1 Prerequisites and Preliminaries -- Part I Rings and Modules -- 2 Rings, Polynomials, Divisibility -- 3 Polynomial Rings in Several Indeterminates -- 4 More on Modules -- 5 On Representations of Finite Groups -- Part II Integral Domains, Polynomials, Fields -- 6 Prime and Maximal Ideals, Integral Domains -- 7 Fields, Division Rings -- Part III Finitely Generated Modules -- 8 Integrality, Noetherianity -- 9 Finitely Generated Projective Modules -- 10 Finitely Generated Modules Over Dedekind Domains -- 11 Complement on Dedekind Domains -- Part IV Characteristic Zero Linear Representations of Finite Groups -- 12 Monoidal Categories: An Introduction -- 13 Characteristic 0 Representations -- 14 Playing With the Base Field -- 15 Induction and Restriction: Some Applications to Finite Groups -- 16 Brauer's Theorem and Some Applications -- 17 Graded Representations and Characters -- 18 The Drinfeld-Lusztig Double of a Group Algebra.

This textbook provides an introduction to fundamental concepts of algebra at upper undergraduate to graduate level, covering the theory of rings, fields and modules, as well as the representation theory of finite groups. Throughout the book, the exposition relies on universal constructions, making systematic use of quotients and category theory - whose language is introduced in the first chapter. The book is divided into four parts. Parts I and II cover foundations of rings and modules, field theory and generalities on finite group representations, insisting on rings of polynomials and their ideals. Part III culminates in the structure theory of finitely generated modules over Dedekind domains and its applications to abelian groups, linear maps, and foundations of algebraic number theory. Part IV is an extensive study of linear representations of finite groups over fields of characteristic zero, including graded representations and graded characters as well as a final chapter on the Drinfeld-Lusztig double of a group algebra, appearing for the first time in a textbook at this level. Based on over twenty years of teaching various aspects of algebra, mainly at the École Normale Supérieure (Paris) and at Peking University, the book reflects the audiences of the author's courses. In particular, foundations of abstract algebra, like linear algebra and elementary group theory, are assumed of the reader. Each of the of four parts can be used for a course - with a little ad hoc complement on the language of categories. Thanks to its rich choice of topics, the book can also serve students as a reference throughout their studies, from undergraduate to advanced graduate level.

ISBN: 9783031500626

Standard No.: 10.1007/978-3-031-50062-6doiSubjects--Topical Terms:

516203
Algebra.

LC Class. No.: QA152.3

Dewey Class. No.: 512

From rings and modules to Hopf algebras = one flew over the algebraist's nest /
LDR:03637nmm a2200325 a 4500 001 2369216
003 DE-He213
005 20240130120151.0
006 m d
007 cr nn 008maaau
008 241127s2024 sz s 0 eng d
020 $a 9783031500626 $q (electronic bk.)
020 $a 9783031500619 $q (paper)
024 7 $a 10.1007/978-3-031-50062-6 $2 doi
035 $a 978-3-031-50062-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA152.3
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
090 $a QA152.3 $b .B875 2024
100 1 $a Broue, Michel. $3 709081
245 1 0 $a From rings and modules to Hopf algebras $h [electronic resource] : $b one flew over the algebraist's nest / $c by Michel Broue.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2024.
300 $a x, 533 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a 1 Prerequisites and Preliminaries -- Part I Rings and Modules -- 2 Rings, Polynomials, Divisibility -- 3 Polynomial Rings in Several Indeterminates -- 4 More on Modules -- 5 On Representations of Finite Groups -- Part II Integral Domains, Polynomials, Fields -- 6 Prime and Maximal Ideals, Integral Domains -- 7 Fields, Division Rings -- Part III Finitely Generated Modules -- 8 Integrality, Noetherianity -- 9 Finitely Generated Projective Modules -- 10 Finitely Generated Modules Over Dedekind Domains -- 11 Complement on Dedekind Domains -- Part IV Characteristic Zero Linear Representations of Finite Groups -- 12 Monoidal Categories: An Introduction -- 13 Characteristic 0 Representations -- 14 Playing With the Base Field -- 15 Induction and Restriction: Some Applications to Finite Groups -- 16 Brauer's Theorem and Some Applications -- 17 Graded Representations and Characters -- 18 The Drinfeld-Lusztig Double of a Group Algebra.
520 $a This textbook provides an introduction to fundamental concepts of algebra at upper undergraduate to graduate level, covering the theory of rings, fields and modules, as well as the representation theory of finite groups. Throughout the book, the exposition relies on universal constructions, making systematic use of quotients and category theory - whose language is introduced in the first chapter. The book is divided into four parts. Parts I and II cover foundations of rings and modules, field theory and generalities on finite group representations, insisting on rings of polynomials and their ideals. Part III culminates in the structure theory of finitely generated modules over Dedekind domains and its applications to abelian groups, linear maps, and foundations of algebraic number theory. Part IV is an extensive study of linear representations of finite groups over fields of characteristic zero, including graded representations and graded characters as well as a final chapter on the Drinfeld-Lusztig double of a group algebra, appearing for the first time in a textbook at this level. Based on over twenty years of teaching various aspects of algebra, mainly at the École Normale Supérieure (Paris) and at Peking University, the book reflects the audiences of the author's courses. In particular, foundations of abstract algebra, like linear algebra and elementary group theory, are assumed of the reader. Each of the of four parts can be used for a course - with a little ad hoc complement on the language of categories. Thanks to its rich choice of topics, the book can also serve students as a reference throughout their studies, from undergraduate to advanced graduate level.
650 0 $a Algebra. $3 516203
650 0 $a Hopf algebras. $3 706147
650 2 4 $a Field Theory and Polynomials. $3 891077
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Category Theory, Homological Algebra. $3 899944
650 2 4 $a Commutative Rings and Algebras. $3 891076
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-50062-6
950 $a Mathematics and Statistics (SpringerNature-11649)