I am a student, prepping for a final exam in graduate Abstract Algebra.
My professor has told me that he will be giving us the following two problems in class to turn in:
(1) Given that R is an integral domain with "said condition", show that if this 'said condition' is true, then R is field if and only if "this is true"
(2) Given that R is a commutative ring with $1 \ne 0$, prove that "some property involving a unit" is true. Or if it is a proper ideal, then it is a non-unit.
I can bring one page of theorems/notes in class to solve these two proposed questions.
My question to everyone is this: If you were presented with these hints towards a final exam, what would you put in your notes to help you solve these questions? What is your thinking process on why it is needed?