Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T10:18:48.656Z Has data issue: false hasContentIssue false
This chapter is part of a book that is no longer available to purchase from Cambridge Core

A Guide to this Guide

Fernando Gouvêa
Affiliation:
Colby College
Get access

Summary

In the first chapter I give a brief historical introduction. Its main role is to situate us in what I call the “modern” approach to algebra.

The second and third chapters are about notations, concepts, and words that I will be using throughout. Chapter 2 introduces the language of category theory, while chapter 3 surveys algebraic structures. I use categorical language only where I feel it is really helpful, so readers should feel free to skip chapter 2 and only refer back as needed. It is also possible to skip chapter 3, since most of the definitions introduced there will be repeated later. Some readers, however, have told me that reading chapter 3 gave them a helpful overview of the algebraic landscape, preparing them for the more detailed exploration to follow. One of my themes in that chapter is that ideas build on other ideas and structures get increasingly rich.

Chapters 4, 5, and 6 are the meat of the book. They address, respectively, groups, rings, and fields. Chapter 4 includes the standard results about groups and the basics of representation theory. Rings and modules are treated next, in Chapter 5; this is the longest chapter, since the world of rings and modules is full of variety. The final chapter deals with fields and skew fields, including Galois theory and the Brauer group. Each of these chapters includes more material than some readers will need or want, so I have tried to make it easy for readers to skip around.

Type
Chapter
Information
Publisher: Mathematical Association of America
Print publication year: 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • A Guide to this Guide
  • Fernando Gouvêa, Colby College
  • Book: A Guide to Groups, Rings, and Fields
  • Online publication: 05 April 2013
  • Chapter DOI: https://doi.org/10.5948/UPO9781614442110.002
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • A Guide to this Guide
  • Fernando Gouvêa, Colby College
  • Book: A Guide to Groups, Rings, and Fields
  • Online publication: 05 April 2013
  • Chapter DOI: https://doi.org/10.5948/UPO9781614442110.002
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • A Guide to this Guide
  • Fernando Gouvêa, Colby College
  • Book: A Guide to Groups, Rings, and Fields
  • Online publication: 05 April 2013
  • Chapter DOI: https://doi.org/10.5948/UPO9781614442110.002
Available formats
×