I have few questions about rings concept that i not really sure:

(a)Let $\displaystyle F$ be field. Every ideal in $\displaystyle F[x]$ is a prime ideal.

(b)Let $\displaystyle F$ be field. Every ideal in $\displaystyle F[x]$ is a principal ideal.(I got this one)

(c)If $\displaystyle \delta$ is Euclidean norm on Euclidean domain $\displaystyle D$ then $\displaystyle \delta(a)=\delta(b)$ if $\displaystyle a,b \in D$ are associates.

Please let me know is that correct, little bit of explain is ok. I'm not looking for a proof. Thank you