# Radical of an ideal

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• November 7th 2008, 07:44 PM
roporte
Radical of an ideal
Let I an ideal of a conmutative ring A. We define the radical of I

$\sqrt{I}=\{ x \in A | \exists n such.that. x^n \in I \}$

A) Prove that the radical of I is an ideal
B) Describe the radical of some ideal of $\mathbb{Z}$
C) If $A=K[X_1, \dots, X_n]$ prove that $\sqrt{I}\subset \mathcal{I}(\mathcal{V}(I))$
• November 7th 2008, 07:51 PM
whipflip15