Test preparation, due on September 26

I think the most important theorems out of the ones we've studied are:
-Every field is an integral domain (and the definitions that say that both of those are commutative and have identity)
-The division algorithm
-Properties of rings that don't come from the definition
-Properties of modular arithmetic

I expect to see questions on the exam that are fairly similar to the homework - proofs that are fairly straightforward but require an understanding of the concepts.

Before the exam, I would like to better understand the proof that every finite integral domain is a field (and the related proof that cancellation is valid in an integral domain).  I will need to review those before taking the test.  I would also like to understand quotient fields of integral domains better, but that will probably come as I do the homework due Monday.  (I won't be in class on Monday, but these are things I need to study on my own.)