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Ideal Radicals Question?

asked 2011-03-12 03:07:19 -0500

Steve gravatar image

updated 2011-03-22 04:31:07 -0500

Felix Lawrence gravatar image

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!

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This question is not appropriate for this forum.

niles gravatar imageniles ( 2011-03-12 05:33:57 -0500 )edit

3 answers

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answered 2011-03-12 13:05:53 -0500

kcrisman gravatar image

You may find Math Stackexchange helpful. Dr. Math also likely has something in their archives.

However, this forum is specifically for asking how to do things with Sage mathematics software. We can compute radicals of ideals, which could conceivably help you gain intuition:

sage: P.<x,y,z> = QQ[]
sage: I = Ideal(x+y+z-3,x^2+y^2+z^2-5,x^3+y^3+z^3-7)
sage: I.radical()
Ideal (x + y + z - 3, y^2 + y*z + z^2 - 3*y - 3*z + 2, 3*z^3 - 9*z^2 + 6*z + 2) of Multivariate Polynomial Ring in x, y, z over Rational Field

However, using such forums for homework help is a breach of netiquette - see the FAQ (which has a typo in one of the first lines... sigh).

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we really need to update the FAQ -- there's actually nothing there along the lines of "this forum is specifically for asking how to do things with Sage mathematics software"

niles gravatar imageniles ( 2011-03-13 03:39:43 -0500 )edit

answered 2011-03-12 03:43:30 -0500

Mike Hansen gravatar image

This is not a forum for homework questions. Your question has nothing to do with Sage.

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answered 2011-03-12 03:56:13 -0500

Steve gravatar image

If you know the answer just answer and if not please let others answer. I want to understand it that's all.

Why do you vote negatively for my question? You want me to vote for your questions and answers the same?

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If your question relates to Sage, it has a chance of getting answered here. If not, it won't. You could try asking at;task=list.

John Palmieri gravatar imageJohn Palmieri ( 2011-03-12 11:43:41 -0500 )edit

Er, the question got a downvote because it has nothing to do with this forum. As for places to get help with homework, there's also you might not like them, though, as they prefer to give hints rather than complete solutions. But I see you posted your question in several other locations, and someone was kind enough to help you with it, even if you rather implausibly denied it was homework (but yet mysteriously had an immediate follow-up question which also looked like homework). I'd be kind of interested in knowing what story you have to explain the urgency, other than an imminent due date..

DSM gravatar imageDSM ( 2011-03-12 13:16:44 -0500 )edit

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Asked: 2011-03-12 03:07:19 -0500

Seen: 631 times

Last updated: Mar 12 '11