Hi everyone, this is my first post. Hope you don't mind that I'm using it to ask a homework question.

Here's the problem:

Let .

- Show is a prime ideal.
- Show is not maximal.

For 1), I let and ; that is, . Because is an integral domain, it has no zero divisors; thus, either or must be and hence in . Is this right?

I wasn't sure about 2); can I take or ?

Thanks, Sam