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Let $ d >0 $ be an integer, and let $ I \subset K[x_1,...,x_n] $ be the monomial ideal $$I = ( x_1^{a_1}x_2^{a_2}...x_n^{a_n} : \ \sum_{i=1}^n a_i =d; \ a_i < d\ \forall i).$$

(a) Compute the saturation $ \widetilde{I} $.

(b) The smallest integer $ k $ such that $ I : m^k = I : m^{k+1} $ is called the saturation number of $ I $. What is the saturation number of $ I $?

The saturation $ \widetilde{I} $ of $ I $ is the ideal $ I : m^{\infty} = \bigcup_{k=1}^{\infty} I : m^k$, where $ m = (x_1,...,x_n) $.

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you can give me some hints that is neccessary to solve them – daisy Dec 1 '12 at 0:40

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