TITLE: Maximal ideal in polynomial ring
QUESTION [9 upvotes]: Is it true that the intersection of a maximal ideal in $A[x]$ with $A$ is a maximal ideal in $A$?
Let's say A is Noetherian. I would be surprised if it isn't true but somehow I can't seem to show it. Any help or tip will be appreciated. Thanks!

REPLY [2 votes]: See also my sci.math post [1] for some further discussion and references
[1] sci.math, 22 Apr 2009
http://groups.google.com/group/sci.math/msg/b00f5e1f7397842f
http://google.com/groups?selm=y8zfxg12ckl.fsf%40nestle.csail.mit.edu