Here's a quick way of doing so:
and as is an integral domain, we have that (X) is a prime ideal
Example (2) on page 682 of Dummit and Foote reads as follows:
------------------------------------------------------------------------
(2) For any field k, the ideal (x) in k[x,y] is primary since it is a prime ideal.
... ... etc
----------------------------------------------------------------------------
Now if (x) is prime then obviously (x) is primary BUT ....
How do we show that (x) is prime in k[x, y]?
Would appreciate some help.
Peter