# Primary ideals of the polynomial ring

Consider the polynomial ring $R:=K[X_1,\ldots ,X_n]$ over the field $K$ and let $a_1,\ldots ,a_n\in K$. Then show that, for all choices of $t_1,\ldots ,t_n\in\mathbb{N}$ the ideal $((X_1-a_1)^{t_1},\ldots ,(X_n-a_n)^{t_n})$ of $R$ is primary.

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What is the radical of your ideal? –  Georges Elencwajg Jun 22 '12 at 11:40
...and use Proposition 4.2 of Atiyah-Macdonald. –  Andrea Jun 22 '12 at 16:33
Thanks I got it –  pritam Jun 24 '12 at 12:09