# The saturation of a monomial ideal

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
i suggest you to ask part (b) as a separate question. –  user 1 Apr 2 '14 at 15:24