Algebra : a teaching and source book /

Algebra : a teaching and source book /

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Bibliographic Details
Author / Creator:	Shult, Ernest, author.
Imprint:	Cham : Springer, 2015.
Description:	1 online resource (xxii, 539 pages) : illustrations
Language:	English
Series:	Online access with purchase: Springer (t)
Subject:	Algebra. Algebra.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11095315

Hidden Bibliographic Details
Other authors / contributors:	Surowski, David, 1949- author.
ISBN:	9783319197340 3319197347 3319197339 9783319197333 9783319197333
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed July 21, 2015).
Summary:	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.
Other form:	Printed edition: 9783319197333
Standard no.:	10.1007/978-3-319-19734-0

Table of Contents:

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.