In Chapter 1, Section 4 of Cox et al "Ideals, Varieties and Algorithms, Exercise 3(c) reads as follows:
Prove the following equality of ideals in :
Any help with this problem would be appreciated.
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I will give you one half:
Originally Posted by Deveno I will give you one half:
Your turn. Thanks for the guidance and help Deveno
OK so we want to show that in we have First show that
From Deveno's equations above it follows that
Thus, ... ... ... (1) Now show
We can write
Thus ... ... ... (2)
Equations (1) (2) we have
Last edited by Bernhard; August 2nd 2013 at 04:08 PM.
Note this shows the generators of ideals in Q[x,y] aren't even unique up to units. Also, this is just high-school algebra in fancier clothes.
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