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.
answered May 8, 2013 at 9:38
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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. $\endgroup$– messiMay 9, 2013 at 4:51
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$\begingroup$ @messi This is because there is no clever answer to your question. What Swanson does is purely theoretical and somehow at an asymptotic level. $\endgroup$– user26857May 9, 2013 at 6:33
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$\begingroup$ @YACP, Yes, you are right. But I wish there was something nice and clever one could say, something very explicit. $\endgroup$– messiMay 10, 2013 at 5:27