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Prime Ideals in K[X]


Well-known member
MHB Site Helper
Jun 22, 2012
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.



Well-known member
MHB Math Scholar
Feb 15, 2012
$K[X]$ is a PID. So any ideal is principal.

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