I have been taking Abstract Algebra graduate classes, and we will begin studying Galois theory.
However, since it is a graduate-level course, the teacher has assumed everyone already had taken undergrauate-level algebra. Problem is, I come from an Engineering background, which did not have it.
Needless to say, I am a bit lost on what I need to know. The teacher will do a brief revision on fields, but I do not even know much about rings (I am fairly comfortable with groups though, since we studied it).
So, long story short, my question is: What do I absolutely must know about rings and fields to understand Galois theory?
I would also appreciate any references that may help. I have been reading Artin's Algebra, and Goodman's Algebra: Abstract and Concrete for now.
And, just to clarify, I do intend to learn more about Algebra later on. It is just that I need to keep up with the lectures, so I must learn the necessary things in a really short time.