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Let $k$ be a field, and $R=k[x,y]$.

I'm supposed to find two different minimal primary decompositions of the ideal $(x^2y, y^2x)$.

It's easy to see that one minimal primary decomposition is $(x)\cap(y)\cap(x^2, y^2)$.

My question: What's the second minimal primary decomposition of the above ideal?

EDIT: I've now added the minimality requirement to the question.

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    Is it necessary that they be minimal?2011-05-23
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    For some reason I can't edit my original question, so here is an important change (which answers Qiaochu's question): Yes, the decompositions have to be minimal.2011-05-23
  • 0
    Your accounts have been merged. Since your new account is registered you should no longer have problems with logging in.2011-05-23

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