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Let I = Q_1 n ... n Q_r = J_1 n ... n J_r be two primary decompositions of I.

How can I show the number of irreducible components in each decomposition is the same?

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- #1

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Let I = Q_1 n ... n Q_r = J_1 n ... n J_r be two primary decompositions of I.

How can I show the number of irreducible components in each decomposition is the same?

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matt grime

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Matt, thank you very much for your reply. Yes the result is true. I'm assuming all uniqueness theorems found in say, Dummit and Foote. I figured it would be easier to prove with some theory in place, hence why I have r on both sides. Whether I need this or not I don't know, but I figured it might make things easier.

Any help would be greatly appreciated.

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matt grime

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mathwonk

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i think you need also to assume the decompositions are irredundant, or it is not true.

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