Hi everyone, I am struggling with some ring notation and was wondering if someone could help.
Here's the question I am having trouble with (and I'm sure it's super-easy):

Proving that a subring is not an ideal-1.png

Proving that a subring is not an ideal-2.png

Any tips would be appreciated, I really just want to understand what the question is asking (particularly in regards to the f(0) = f(1) part). I know the conditions that make an ideal, I just don't know how to apply them to this situation.