國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Algebraa teaching and source book /

Shult, Ernest.

Algebraa teaching and source book /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Algebraby Ernest Shult, David Surowski.
其他題名:	a teaching and source book /
作者:	Shult, Ernest.
其他作者:	Surowski, David.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xxii, 539 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Algebra.
電子資源:	http://dx.doi.org/10.1007/978-3-319-19734-0
ISBN:	9783319197340 (electronic bk.)

Algebraa teaching and source book /
Shult, Ernest.

Algebraa teaching and source book /[electronic resource] :by Ernest Shult, David Surowski. - Cham :Springer International Publishing :2015. - xxii, 539 p. :ill., digital ;24 cm.

Basics -- Basic Combinatorial Principles of Algebra -- Review of Elementary Group Properties -- Permutation Groups and Group Actions -- Normal Structure of Groups -- Generation in Groups -- Elementary Properties of Rings -- Elementary properties of Modules -- The Arithmetic of Integral Domains -- Principal Ideal Domains and Their Modules -- Theory of Fields -- Semiprime Rings -- Tensor Products.

This book presents a graduate-level course on modern algebra. It can be used as a teaching book - owing to the copious exercises - and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan-Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.

ISBN: 9783319197340 (electronic bk.)

Standard No.: 10.1007/978-3-319-19734-0doiSubjects--Topical Terms:

188312
Algebra.

LC Class. No.: QA152.3

Dewey Class. No.: 512

Algebraa teaching and source book /
LDR:02434nmm a2200313 a 4500 001 472801
003 DE-He213
005 20160223145414.0
006 m d
007 cr nn 008maaau
008 160316s2015 gw s 0 eng d
020 $a 9783319197340 (electronic bk.)
020 $a 9783319197333 (paper)
024 7 $a 10.1007/978-3-319-19734-0 $2 doi
035 $a 978-3-319-19734-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA152.3
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 512 $2 23
090 $a QA152.3 $b .S562 2015
100 1 $a Shult, Ernest. $3 728095
245 1 0 $a Algebra $h [electronic resource] : $b a teaching and source book / $c by Ernest Shult, David Surowski.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xxii, 539 p. : $b ill., digital ; $c 24 cm.
505 0 $a Basics -- Basic Combinatorial Principles of Algebra -- Review of Elementary Group Properties -- Permutation Groups and Group Actions -- Normal Structure of Groups -- Generation in Groups -- Elementary Properties of Rings -- Elementary properties of Modules -- The Arithmetic of Integral Domains -- Principal Ideal Domains and Their Modules -- Theory of Fields -- Semiprime Rings -- Tensor Products.
520 $a This book presents a graduate-level course on modern algebra. It can be used as a teaching book - owing to the copious exercises - and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan-Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.
650 0 $a Algebra. $3 188312
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Field Theory and Polynomials. $3 274058
700 1 $a Surowski, David. $3 728096
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-19734-0
950 $a Mathematics and Statistics (Springer-11649)