Abstract algebra book recommendations for beginners.

I am taking abstract algebra in this semester. I find that my lecturer didn't provide enough examples for understanding. So I would like to ask what are the recommended books which has lots of solved problems and exercises? The lecturer said in this semester, he will cover group theory, ring theory and a bit of field theory. Which book contains extensive information in these three fields?

Solution 1:

For a one-semester course in abstract algebra: undergraduate/first-course-level, I'd highly recommend Fraleigh's A First Course in Abstract Algebra. It's very well written, very readable, and includes a LOT of examples in the text itself, as well as in the exercises.

Personally, I've found the most success using this text for first-course/semester-length classes.

Another possible aid, in addition to a supplementary text, is Beachy's Abstract Algebra Online Study Guide, where you'll find an extensive study guide and practice problems. It may help to supplement areas where you're feeling weakest. I'll include here, as well, a link for accessing Beachy's ~150 page pdf Abstract Algebra - Study Guide for Beginners available for downloading, freely distributed.

Solution 2:

Dummit & Foote has lots.

But following up on the "Artin" recommendation which is excellent, you can watch these great videos that follow "Artin" and see many examples very nicely articulated. You can probably get a lot more out of these lectures by Benedict Gross at Harvard:

http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

Solution 3:

I suggest you Algebra Through Practice collection by T. S. Blyth for first step and then Herstein or Fraleigh are good.

Solution 4:

Michael Artin's book Algebra is very nice.