When I study a subject I normally use a main text and one or more companion texts. I consult these companion texts to help me out if I get stuck on a concept or to provide more examples if needed.
I'm currently working my way through Algebra: Chapter 0 by Aluffi and I am looking for suggestions for companion volumes. I purchased the two volumes by Jacobson, Basic Algebra I and II, as they are inexpensive and have a good reputation. I'm looking for one more good, solid graduate abstract algebra textbook. I'm considering either:
- Basic Algebra & Advanced Algebra by Anthony Knapp
- Abstract Algebra 2nd Edition by Pierre Grillet
Can anyone comment on the texts by these two authors? If you also have familiarity with Aluffi's text and how they would synergize with it that would be a bonus.
Aluffi's book is already thick and it can barely introduce some subjects. As far as I've gone through that book, it is self contained and very detailed so in my opinion it doesn't need another book to make comparisons. Jacobson's books are huge and you would need a very long time to read them. Same goes for Grillet, which is more of a reference than a book for a beginner.
Read for example this blog post on documentation. When you start learning algebra you need something like an how-to instead of a thousand long treatise on every-possible-thing-you-might-want-to-know-from-one-of-the-biggest-areas-of-math. One complement you might want to consider are lecture notes from a university.
You would eventually need other books (or sources) to get into category theory or commutative algebra or homological algebra or other topics, as Aluffi's book does not have anough room to treat them in details (it is a book that introduces the reader to the broad area of algebra), but that is a different question.