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Algebraa teaching and source book /

Shult, Ernest.

Algebraa teaching and source book /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Algebraby Ernest Shult, David Surowski.
Reminder of title:	a teaching and source book /
Author:	Shult, Ernest.
other author:	Surowski, David.
Published:	Cham :Springer International Publishing :2015.
Description:	xxii, 539 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Algebra.
Online resource:	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 /
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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)