Cengage/Higher Education/Post-Calculus/Abstract Algebra: An Introduction
Return to search
Abstract Algebra: An Introduction book cover
Student viewInstructor view

Abstract Algebra: An Introduction

By Thomas W. Hungerford

3rd Edition © 2013
Discipline:Mathematics
Course:Post-Calculus
Starting from$71.99
See pricing details and explore formats

Get your course materials

Cengage Unlimited

Get day-one access to course content, AI-powered support, and resources to build college and career-ready skills.

Manage Subscription

eBook

Get instant access to your course content on the device of your choice, with built-in tools like highlighting, bookmarking, and search.

Paperback

Buy or Rent the textbook

Get a new, printed copy of your textbook, ready for notes and highlighting. Plus, free shipping and returns on orders. *See terms and conditions.

Added to cart.
Something went wrong. Please try again.

Questions about this product?

Get help with product, platform or format questions.

Let’s connect
Explore instructor resources

About your course materials

Abstract Algebra: An Introduction is set apart by its thematic development and organization. The chapters are organized around two themes: arithmetic and congruence. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups. This enables students to see where many abstract concepts come from, why they are important, and how they relate to one another. New to this edition is a "groups first" option that enables those who prefer to cover groups before rings to do so easily.

Frequently asked questions

How do I enroll in or join my course?

Your instructor will tell you how to access your course. You may join through your school’s LMS, a course link or a course key. If you’re unsure which method to use, check with your instructor.

How do I redeem an access code, or what if my code isn't working?

Sign in to your Cengage account and select Enter Access Code or Course Key, then enter your access code and select Register. If your code is damaged, missing or still doesn't work, contact Cengage Support.

Why can't I access my course?

How you access your course depends on how your instructor set it up. Start from your LMS, course link or course key. If you've purchased access but still can't open the course, Cengage Help can help you troubleshoot your access.

Where can I find my eBook or textbook?

You can access available eBooks from your Cengage student dashboard or from your Cengage course. If your class uses an LMS, your instructor may also provide access there.

What if I don't have access to my course materials yet?

Temporary access may be available for some Cengage courses. If offered, you can use your course during the grace period and purchase or register your access code before it ends. Options for expired access vary by product.

AboutTable of contentsResourcesPricing & formatsRelated products

About this product

Abstract Algebra: An Introduction is set apart by its thematic development and organization. The chapters are organized around two themes: arithmetic and congruence. Each theme is developed first for the integers, then for polynomials, and finally for rings and groups. This enables students to see where many abstract concepts come from, why they are important, and how they relate to one another. New to this edition is a "groups first" option that enables those who prefer to cover groups before rings to do so easily.

The text may be used for either courses that cover rings before groups (as in earlier editions) OR courses that cover groups before rings.

The flexible design of this text makes it suitable for courses of various lengths and different levels of mathematical sophistication.

The chapters are organized around two themes, arithmetic and congruence, that are developed first for the integers and then for rings, polynomials, and groups.

The emphasis throughout is on clarity of exposition.

Table of contents

Chapters

Cover
EP1
EP2
Title
Statement
Copyright
Dedication
Table of Contents
Preface
To the Instructor
To the Student
Thematic Table of Contents for the Core Course
Part 1: The Core Course
Part 2: Advanced Topics
Part 3: Excursions and Applications
Part 4: Appendices
Bibliography
Answers and Suggestions for Selected Odd-Numbered Exercises
Index
EP3
EP4
Show more

Part 1: The Core Course

Ch 1: Arithmetic in Z Revisited
Preview this section ↗
Introduction ↗
1.1 The Division Algorithm ↗
1.2 Divisibility ↗
1.3 Primes and Unique Factorization ↗
Ch 2: Congruence in Z and Modular Arithmetic
Introduction
2.1 Congruence and Congruence Classes
2.2 Modular Arithmetic
2.3 The Structure of Zp (p Prime) and Zn
Ch 3: Rings
Introduction
3.1 Definition and Examples of Rings
3.2 Basic Properties of Rings
3.3 Isomorphisms and Homomorphisms
Ch 4: Arithmetic in F[x]
Introduction
4.1 Polynomial Arithmetic and the Division Algorithm
4.2 Divisibility in F[x]
4.3 Irreducibles and Unique Factorization
4.4 Polynomial Functions, Roots, and Reducibility
4.5 Irreducibility in Q[x]
4.6 Irreducibility in R[x] and C[x]
Ch 5: Congruence in F[x] and Congruence-Class Arithmetic
Introduction
5.1 Congruence in F[x] and Congruence Classes
5.2 Congruence-Class Arithmetic
5.3 The Structure of F[x]/(p(x)) When p(x) Is Irreducible
Ch 6: Ideals and Quotient Rings
Introduction
6.1 Ideals and Congruence
6.2 Quotient Rings and Homomorphisms
6.3 The Structure of R/I When I Is Prime or Maximal
Ch 7: Groups
Introduction
7.1 Definition and Examples of Groups
7.1.A Definition and Examples of Groups
7.2 Basic Properties of Groups
7.3 Subgroups
7.4 Isomorphisms and Homomorphisms
7.5 The Symmetric and Alternating Groups
Ch 8: Normal Subgroups and Quotient Groups
Introduction
8.1 Congruence and Lagrange’s Theorem
8.2 Normal Subgroups
8.3 Quotient Groups
8.4 Quotient Groups and Homomorphisms
8.5 The Simplicity of An

Resources

Instructor resources for this title can include manuals, test banks, educator guides, multimedia and companion sites. Sign in to see what is available.

Instructor manuals
Test banks
Educator guides
Multimedia
Companion sites
Sign in to view & download

Pricing and formats

Learning Platforms
eBook
Paperback
Bundle

Give students more with Cengage Unlimited

Choose the Cengage content and Learning Platform that fit your course while giving students access to Cengage Learning Platforms and our entire eBook library with one subscription.

4-12 month student access

$169.99 – $244.99

eBook

Give students digital access to textbook content with tools to highlight, bookmark and search as they read.

6 months

ISBN-13: 9781285374314
$71.99

12 months

ISBN-13: 9781285374314
$98.99
Sign in to view & adopt this title

Paperback

Purchase

ISBN-13: 9780357670873
$232.95
Sign in to view & adopt this title

Related products

Linear Algebra: A Modern Introduction book cover
Higher Education

Linear Algebra: A Modern Introduction

David Poole
5th Edition © 2026
Loose-leaf
Paperback
WebAssign
Starting from
$71.99
View details
Differential Equations with Boundary-Value Problems book cover
Higher Education

Differential Equations with Boundary-Value Problems

Dennis G. Zill
10th Edition © 2024
Hardback
Media Options
WebAssign
Starting from
$71.99
View details
A First Course in Differential Equations with Modeling Applications book cover
Higher Education

A First Course in Differential Equations with Modeling Applications

Dennis G. Zill
12th Edition © 2024
Hardback
WebAssign
eBook
Starting from
$71.99
View details
Elementary Linear Algebra book cover
Higher Education

Elementary Linear Algebra

Ron Larson
8th Edition © 2017
Hardback
Paperback
WebAssign
Starting from
$54.00
View details
Numerical Analysis book cover
Higher Education

Numerical Analysis

J. Douglas Faires
10th Edition © 2016
Hardback
MindTap
eBook
Starting from
$71.99
View details
A Transition to Advanced Mathematics book cover
Higher Education

A Transition to Advanced Mathematics

Doug Smith, Maurice Eggen, Richard St. Andre
8th Edition © 2015
Hardback
WebAssign
eBook
Starting from
$71.99
View details

This product is provided solely for instructional purposes, and your use of this product is governed by Cengage's Terms of Use. By using this product, you acknowledge your obligation to comply with these terms. View Terms of Use.

Cengage support team
Cengage support team

Still need support?

Get help with course access, registration, purchases or technical issues from Cengage Support.
Contact support
Cengage support team
Cengage support team

Need help?

Connect with us today, and let’s explore how we can support your goals.
Get in touch
Cengage
Higher Education
K–12
Higher Education

Higher Education

Future-focused tools to teach, learn, and build career-ready skills.
Get started

Students

Instructors

Leaders

Librarians

Career and Workforce
Sign In

Higher Education

Student
Instructor
Gale
ELL
Name
Dashboard
Profile
Sign Out
Support

Recent searches

Chemistry
Mindtap Biology
Calculus
Recent query

Suggestions

Calculus230 results
Calculus Early Transcendentals84 results
Calculus Concepts37 results
Suggestion0 results

Matching products

2 results
Abstract navy to teal gradient placeholder
TAGTAGTAG
9th Edition•© 2021

Calculus: Early Transcendentals

James Stewart, Daniel K. Clegg and Saleem Watson

Abstract navy to teal gradient placeholder
TAGTAGTAG
9th Edition•© 2021

Calculus

James Stewart, Daniel K. Clegg and Saleem Watson

TAG
Edition

Product title

Authors
No matching products. Press Enter to search the full catalog.
Product suggestions are unavailable right now. Press Enter to search the full catalog.
Searching…
Sign In

Higher Education

Student
Instructor
Gale
ELL
Name
Dashboard
Profile
Sign Out
Your basket (3)
eTextbook: Calculus | 12th Edition
eTextbook Access: 360 days
$76.99
Cengage Unlimited - Full - Multi-Term Access (12 months)
Digital Access: 365 days
$124.99
Introduction to Physical Anthropology | 15th Edition
Textbook
$124.99
This is some text inside of a div block.
This is some text inside of a div block.
This is some text inside of a div block.
Your basket is empty.
We couldn’t load your basket. Please try again.
Loading your basket…
Total:
$201.98
I’m ready to checkout
Get Support
US
Change Country
Students

Students

See Overview

Access & Use Products

Access Instructions
Help Center

Get Help

Instructors

Instructors

See Overview

Products

Disciplines
Learning Platforms
Cengage Unlimited

Access & Use Products

Instructor Support
Course Setup
Training
Help Center

Get help

Leaders & Admins

Leaders & Admins

See Overview

Programs

Cengage Unlimited
Gale

Access & Use Products

LMS Integration

Resources

Published Research
Help Center

Get help

Librarians

Librarians

See Overview

Products

Databases
Primary Sources
Digital Humanities Tools
eLearning

Access & Use Products

Discovery Services
Gale Support
Gale Support

Get Support

Find Your Local Cengage Site

Select country
🇦🇫
Afghanistan
🇦🇱
Albania
🇩🇿
Algeria
🇦🇩
Andorra
🇦🇴
Angola
🇦🇮
Anguilla
🇦🇬
Antigua and Barbuda
🇦🇷
Argentina
🇦🇲
Armenia
🇦🇼
Aruba
🇦🇺
Australia
🇦🇹
Austria
🇦🇿
Azerbaijan
🇧🇸
Bahamas
🇧🇭
Bahrain
🇧🇩
Bangladesh
🇧🇧
Barbados
🇧🇾
Belarus
🇧🇪
Belgium
🇧🇿
Belize
🇧🇯
Benin
🇧🇲
Bermuda
🇧🇹
Bhutan
🇧🇴
Bolivia
🇧🇦
Bosnia and Herzegovina
🇧🇼
Botswana
🇧🇷
Brazil
🇻🇬
British Virgin Islands
🇧🇳
Brunei
🇧🇬
Bulgaria
🇧🇫
Burkina Faso
🇧🇮
Burundi
🇰🇭
Cambodia
🇨🇲
Cameroon
🇨🇦
Canada
🇨🇻
Cape Verde
🇰🇾
Cayman Islands
🇨🇫
Central African Republic
🇹🇩
Chad
🇨🇱
Chile
🇨🇳
China
🇨🇴
Colombia
🇰🇲
Comoros
🇨🇰
Cook Islands
🇨🇷
Costa Rica
🇨🇮
Côte d'Ivoire
🇭🇷
Croatia
🇨🇺
Cuba
🇨🇾
Cyprus
🇨🇿
Czech Republic
🇨🇩
Democratic Republic of the Congo
🇩🇰
Denmark
🇩🇯
Djibouti
🇩🇲
Dominica
🇩🇴
Dominican Republic
🇪🇨
Ecuador
🇪🇬
Egypt
🇸🇻
El Salvador
🇬🇶
Equatorial Guinea
🇪🇷
Eritrea
🇪🇪
Estonia
🇸🇿
Eswatini
🇪🇹
Ethiopia
🇫🇰
Falkland Islands (Malvinas)
🇫🇴
Faroe Islands
🇫🇯
Fiji
🇫🇮
Finland
🇫🇷
France
🇬🇫
French Guiana
🇬🇪
Georgia
🇩🇪
Germany
🇬🇭
Ghana
🇬🇮
Gibraltar
🇬🇷
Greece
🇬🇱
Greenland
🇬🇩
Grenada
🇬🇵
Guadeloupe
🇬🇺
Guam
🇬🇹
Guatemala
🇬🇳
Guinea
🇬🇼
Guinea-Bissau
🇬🇾
Guyana
🇭🇹
Haiti
🇭🇳
Honduras
🇭🇰
Hong Kong
🇭🇺
Hungary
🇮🇸
Iceland
🇮🇳
India
🇮🇩
Indonesia
🇮🇷
Iran
🇮🇶
Iraq
🇮🇪
Ireland
🇮🇱
Israel
🇮🇹
Italy
🇯🇲
Jamaica
🇯🇵
Japan
🇯🇴
Jordan
🇰🇿
Kazakhstan
🇰🇪
Kenya
🇰🇮
Kiribati
🇰🇼
Kuwait
🇰🇬
Kyrgyzstan
🇱🇦
Laos
🇱🇻
Latvia
🇱🇧
Lebanon
🇱🇸
Lesotho
🇱🇷
Liberia
🇱🇮
Liechtenstein
🇱🇹
Lithuania
🇱🇺
Luxembourg
🇲🇴
Macau
🇲🇬
Madagascar
🇲🇼
Malawi
🇲🇾
Malaysia
🇲🇻
Maldives
🇲🇱
Mali
🇲🇹
Malta
🇲🇭
Marshall Islands
🇲🇶
Martinique
🇲🇷
Mauritania
🇲🇺
Mauritius
🇲🇽
Mexico
🇲🇩
Moldova
🇲🇨
Monaco
🇲🇳
Mongolia
🇲🇪
Montenegro
🇲🇸
Montserrat
🇲🇦
Morocco
🇲🇿
Mozambique
🇲🇲
Myanmar
🇳🇦
Namibia
🇳🇷
Nauru
🇳🇵
Nepal
🇳🇱
Netherlands
🇳🇿
New Zealand
🇳🇮
Nicaragua
🇳🇪
Niger
🇳🇬
Nigeria
🇳🇺
Niue
🇰🇵
North Korea
🇲🇰
North Macedonia
🇳🇴
Norway
🇴🇲
Oman
🇵🇰
Pakistan
🇵🇼
Palau
🇵🇸
Palestine
🇵🇦
Panama
🇵🇬
Papua New Guinea
🇵🇾
Paraguay
🇨🇬
People's Republic of Congo
🇵🇪
Peru
🇵🇭
Philippines
🇵🇱
Poland
🇵🇹
Portugal
🇵🇷
Puerto Rico
🇶🇦
Qatar
🇷🇴
Romania
🇷🇺
Russia
🇷🇼
Rwanda
🇼🇸
Samoa
🇸🇲
San Marino
🇸🇹
Sao Tome and Principe
🇸🇦
Saudi Arabia
🇸🇳
Senegal
🇷🇸
Serbia
🇸🇨
Seychelles
🇸🇱
Sierra Leone
🇸🇬
Singapore
🇸🇰
Slovakia
🇸🇮
Slovenia
🇸🇧
Solomon Islands
🇸🇴
Somalia
🇿🇦
South Africa
🇰🇷
South Korea
🇪🇸
Spain
🇱🇰
Sri Lanka
🇰🇳
St. Kitts and Nevis
🇱🇨
St. Lucia
🇵🇲
St. Pierre and Miquelon
🇻🇨
St. Vincent & The Grenadines
🇸🇩
Sudan
🇸🇷
Suriname
🇸🇯
Svalbard and Jan Mayen Islands
🇸🇪
Sweden
🇨🇭
Switzerland
🇸🇾
Syria
🇹🇼
Taiwan
🇹🇯
Tajikistan
🇹🇿
Tanzania
🇹🇭
Thailand
🇹🇱
Timor-Leste
🇹🇬
Togo
🇹🇰
Tokelau
🇹🇴
Tonga
🇹🇹
Trinidad and Tobago
🇹🇳
Tunisia
🇹🇷
Turkey
🇹🇲
Turkmenistan
🇹🇨
Turks and Caicos Islands
🇹🇻
Tuvalu
🇺🇬
Uganda
🇺🇦
Ukraine
🇦🇪
United Arab Emirates
🇬🇧
United Kingdom
🇺🇸
United States
🇺🇾
Uruguay
🇺🇿
Uzbekistan
🇻🇺
Vanuatu
🇻🇦
Vatican
🇻🇪
Venezuela
🇻🇳
Vietnam
🇪🇭
Western Sahara
🇾🇪
Yemen
🇿🇲
Zambia
🇿🇼
Zimbabwe
Cengage

Welcome to Cengage

It looks like you’re visiting from another country. Would you like to visit your local Cengage site instead?

Cengage logo

Support

(800) 354-9706

support.cengage.com

K–12

Higher Education

Career and Workforce

Students

Instructors

Leaders & Admin

Librarians

Company

About

News

Research & Outcomes

Investors

Careers

Content Development Philosophy

Authors/Royalties

Cengage AI

Contact

Contact Us

Support

ServicePlus Ordering

© 2020 Cengage Learning, Inc. and its affiliates

Copyright

Privacy

Piracy

Terms of Use

Accessibility

Compliance & Ethics

Do Not Sell