Primary decomposition of $I = (x^2, y^2, xy)$

Question

I want to find a primary decomposition of the ideal $$ I = (x^2,y^2,xy) \subset k[x,y]$$ where $k$ is a field.

How to proceed? Are there algorithms to find such decompositions? Where can I find them?

In fact this ideal is already primary, being a power of the maximal ideal $(x,y)$ — zcn, Jun 15 '14 at 19:30
zcn is right, but for algorithm and the use of it i wrote the answer below. — , Jun 16 '14 at 05:57

score 1 · Accepted Answer · edited May 21 '16 at 10:19

1

Yes, there are algorithms to find such decompositions in the book "Monomial Ideals" by "Jürgen Herzog-Takayuki Hibi":

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(I deleted the proof of uniqueness)

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so

$I = (x^2, y^2, xy)= ( y^2, x) \cap (x^2, y)$

edited May 21 '16 at 10:19

user26857

answered Jun 15 '14 at 09:59

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As it was mentioned under the question $I$ is already primary. – user26857 May 21 '16 at 10:21

1 Answers1