Prime Ideals in K[X]

[Peter]

I am reading R.Y.Sharp's book: "Steps in Commutative Algebra.

In Chapter 3: Prime Ideals and Maximal Ideals, Exercise 3.22 (ii) reads as follows:

-------------------------------------------------------------------------

Determine all the prime ideals of the ring K[X],

where K is a field and X is an indeterminate.

------------------------------------------------------------------------

Can someone please help me get started on this problem.

Peter

 

[Deveno]

$K[X]$ is a PID. So any ideal is principal.

If $P = (f(X))$ is prime, what can you say about $f(X)$?