a second course in abstract algebra

Question

I recently read an abstract algebra textbook, "A first course in abstract algebra" by John Fraleigh. I am interested in continuing to do some more self studying. What is a good book for a second course in the subject for self studying? Thanks.

Answer 1

I used Fraleigh in the first course in algebra I ever took. Then I used Hungerford's Algebra for several additional courses (as a student). I think Hungerford is the best abstract algebra text I have ever seen. I strongly recommend it. It's in Springer's GTM (Graduate Texts in Mathematics) series.

Addendum: But Hungerford is no slim text. It's a honkin' bible.

Answer 2

Michael Artin's Algebra is a great choice. It is pretty advanced for an undergrad book, but very well-written, and at times even humorous or entertaining. It's amazing that Artin manages to discuss so much material in this slim book--he even reviews some abstract linear algebra. It has an introduction to Galois theory at the end.

You can also check out the classic texts by Herstein and Jacobson (the latter is usually used by first-year grad students).

Answer 3

I agree with StrangerLoop's response. I learned what I know about Galois theory from Artin's Algebra, and it had a reasonable amount of depth while being understandable at the same time.

Now that I've actually completed two semesters of undergrad abstract algebra, I've found Dummit and Foote to be a rather approachable text as well. I can see how certain sections of Dummit and Foote can be too advanced for the first time through, but it's been very pleasant going back and adding depth to material I've previously been introduced to.