I am taking a graduate level algebra course.  We are using the
textbook Algebra by Serge Lang, 3rd edition.  I find this textbook
quite dense, and want some online resources.  It is a commonly used
textbook for this level course.  The type of things I had in mind
include solutions to problems, additional explanation of the proofs in
the text, errata sheets, survival tips, etc.

I was using google in hopes of finding some helpful information.  The
search is difficult because Lang has written many books and several of
the others have the word algebra in their title.  To make things
worse, lang is often used as an abbreviation for language, so I am
getting irrelevant links to sort through.

To make sure we are talking about the same book, it is published by
Addison-Wessley with ISBN 0-201-55540-9.

Hi there!

This was a tricky one - there's a book of published answers to Lang's
*Linear* Algebra book, but no equivalent for his Algebra book.
However, a search on Google using the terms "solutions Lang's Algebra"
led me to this page:

http://math.berkeley.edu/~ribet/Math250/index.html

This is the website of Professor Ken Ribet, a mathematics professor at
the University of California, Berkeley. He uses the 3rd edition of
Serge Lang's Algebra as the core text-book for his course, and at the
foot his page you'll find solutions to all the questions he's set his
students from this book.

For example, in the first week of his course he set people questions
1, 3, 4, 5, 6, 7 and 9 from Chapter One, and so he provides full
solutions to these on his site. He also includes worked solutions to
typical exams on the same work, which could be helpful if you're
working through similar problems.

Professor Ribet also provides a link to a colleague's website:

http://math.berkeley.edu/~gbergman/.C.to.L/index.html

Put together by Professor George Bergman, this is an unofficial
companion to Lang's Algebra, containing additional notes to selected
chapters. As he says in his introductory note, "I attempt to bring
together in an orderly arrangement materials I have given to my
classes over the years when teaching Berkeley's graduate algebra
course, Math 250, from Lang's Algebra - motivations, explanations,
supplementary results and examples, advice on material to skip, etc..
I follow this expository material with some exercises not in the text
that I particularly like, together with notes on a few of the
exercises in the text."

I think you should find this quite helpful - and Professor Bergman
also provides errata to the current volume of "Algebra".

In order to view Professor Ribet's solutions, you'll need Adobe
Acrobat Reader. If you don't already have this, you can download it
at:
http://www.adobe.com/support/downloads/main.html#Readers

In order to view Professor Bergman's notes, you'll need GhostScript
and GhostScript Viewer, available from:
http://www.cs.wisc.edu/~ghost/doc/AFPL/get704.htm
... or directly at the following URLs:
ftp://mirror.cs.wisc.edu/pub/mirrors/ghost/AFPL/gs704/gs704w32.exe
(GhostScript)
ftp://mirror.cs.wisc.edu/pub/mirrors/ghost/ghostgum/gsv43w32.exe
(Viewer)

I hope this answers your question satisfactorily - good luck with your
algebra work!

Best wishes,
stuartwoozle-ga

I have always felt like Rotman's "Introduction to the theory of
groups" is a terrific book; not only for understanding group theory,
but also for field theory and ring theory (as there is a section on
Galois theory). The Lang text, I agree, would benefit from a corpus of
examples to help build intuition about his somewhat abstract
presentation.

Rutgers has used Hungerford and Jacobson for abstract algebra at the graduate
level, as well as Lang.  Of the three, I'd highly recommend Hungerford for
clarity.  Lang's book is more of a reference book, and Jacobson's text suffers
from numerous problems (most notable of which is an extremely poor index).
Herstein's undergraduate text is quite a good foundational text if your
background in abstract algebra is weak, but it's most valuable for it's
excellent and numerous problems.  As with any branch of mathematics, you
need to spend a great deal of time solving lots of problems to completely
grasp the subject.

-Chris