Is it possible to learn ring theory if one's familiar, but not good at group theory? [closed]
Is it possible to learn ring theory if one's familiar, but not good at group theory?
Absolutely yes; your study of Dummit and Foote should give you enough of a foundation in "group theory" to successfully study "ring theory" in greater depth. So it is indeed possible to learn ring theory before being fully proficient in group theory.
But I also want to add:
It is far too early for you to conclude you are not good at group theory!
You're an undergrad, as you point out, and your experience when first encountering any new theory or topic is not really sufficient evidence to determine how "good" you are at it, especially if you're making that judgment based on your progress through one book's coverage of groups.
Every serious student of math encounters a wall at one point or another (and for most of us, many many times). Sometimes the things that first "trip us up" are precisely the things that end up fascinating us.
Furthermore, try not to judge your mastery of any topic (e.g. group theory) based on its presentation in only one text. (In my humble opinion) Dummit and Foote's text is not all that great in covering groups.
So explore a bit by supplementing Dummit and Foote's coverage of groups with other resources: e.g., find a text or two that approach groups differently:
Artin's Algebra covers groups well; see especially chapter 2.
Or - if you're really struggling with groups - try looking at Fraleigh's A First Course in Algebra, which does great with introducing groups and motivating the material. The book is written in a way that is very readable, intuitive, and includes a lot of examples.
If you can't access one of the above texts through a library, and are looking to limit expense, J.S. Milne has a nice site for course-notes, including a ~$140$-page pdf on Group Theory.
So try not to "write off" group theory quite yet; you may find you like group theory, after all!
It is certainly possible to study rings before groups. In fact, this is the approach taken in say Shifrin's Abstract Algebra as rings are perhaps more natural than groups to some.
On the other hand, the study of rings will involve some group-theoretic results, but these can always be picked up on the go.
Personally, I think "Dummit & Foote" is excellent for ring theory. And much more accessible for a beginner than groups. (Dummit wrote rings, Foote groups.)
To build more confidence in groups, the chapter in Artin's "Algebra" (go for the 2nd edition) on groups is very well written and can give a very intuitive understanding of what are key points.
You can also watch the specific videos on groups in this excellent lecture series by Benedict Gross at Harvard, that follow Artin. You will most likely want to watch the ones on rings as you study that topic.
http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra