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Let $R$ be a commutative Noetherian ring with unit. Suppose $P$ is a prime ideal that is not maximal. How can we go about finding a normal (reduced) primary decomposition of the power of $P$, say a normal decomposition for $P^2$ or $P^3$?

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I was just recently looking into symbolic powers and primary decompositions, and I remember looking at this script. It didn't really help me with my question, but I think that section 8 might be of perfect use to you. You might find more texts by Swanson on the topic, she has done some very nice work in that area.

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  • $\begingroup$ I had looked up that article, but still i dont have a good feeling on how to get a primary decomposition of a power of a prime in a specific example say. But thanks. $\endgroup$ – messi May 9 '13 at 4:51
  • $\begingroup$ @messi This is because there is no clever answer to your question. What Swanson does is purely theoretical and somehow at an asymptotic level. $\endgroup$ – user26857 May 9 '13 at 6:33
  • $\begingroup$ @YACP, Yes, you are right. But I wish there was something nice and clever one could say, something very explicit. $\endgroup$ – messi May 10 '13 at 5:27

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