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Abstract algebra an introductory course

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This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields.
The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions.

Contents
Part I Preliminaries
1 Relations and functions
2 The integers and modular arithmetic

Part II Groups
3 Introduction to groups
4 Factor groups and homomorphisms
5 Direct products and the classification of finite abelian groups
6 Symmetric and alternating groups
7 The sylow theorens

Part III Rings
8 Introduction to rings
9 Ideals, factor rings and homomorphisms
10 Special types of domains

Part IV Fields and polynomials
11 Irreducible polynomials
12 Vector spaces and field extensions

Part V Applications
13 Public key cryptography
14 Straightedge and compass constructions
Index

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Availability

Detail Information

Series Title

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Call Number

512 LEE a

Publisher

Canada : Springer., 2010

Collation

301 hlm.; 25 cm

Language

English

ISBN/ISSN

9783319776484

Classification

512

Content Type

-

Media Type

-

Carrier Type

-

Edition

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Subject(s)

Algebra, Abstract

Specific Detail Info

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Statement of Responsibility

Gregory T. Lee

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