# Ideal Radicals Question

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• March 12th 2011, 07:47 AM
DukeSteve
Ideal Radicals Question
Hello experts,

Given that there is a commutative ring R and 2 ideals I and J, also given that I is included in J

I need to prove
1) radical of I is in radical of J
2) radical of radical of ideal I = radical of ideal I.

Please give me a detailed answer, I need it urgently!!!!

Thanks in advance!
• March 12th 2011, 09:32 AM
Tinyboss
These are both immediate from the definition of the radical of an ideal. Do you understand the definition? Have you tried to write down precise statements of (1) and (2) in terms of that definition? That's essentially all this problem calls for.
• March 12th 2011, 09:38 AM
FernandoRevilla
A tiny hint:

$I\subset \textrm{rad}(I)$