ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 13 Mar 2011 09:39:43 +0100Ideal Radicals Question?https://ask.sagemath.org/question/7990/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!Sat, 12 Mar 2011 10:07:19 +0100https://ask.sagemath.org/question/7990/ideal-radicals-question/Comment by niles for <p>Hello experts,</p>
<p>Given that there is a commutative ring R and 2 ideals I and J, also given that I is included in J</p>
<p>I need to prove
1) radical of I is in radical of J
2) radical of radical of ideal I = radical of ideal I.</p>
<p>Please give me a detailed answer, I need it urgently!!!!</p>
<p>Thanks in advance!</p>
https://ask.sagemath.org/question/7990/ideal-radicals-question/?comment=22008#post-id-22008This question is not appropriate for this forum.Sat, 12 Mar 2011 12:33:57 +0100https://ask.sagemath.org/question/7990/ideal-radicals-question/?comment=22008#post-id-22008Answer by Mike Hansen for <p>Hello experts,</p>
<p>Given that there is a commutative ring R and 2 ideals I and J, also given that I is included in J</p>
<p>I need to prove
1) radical of I is in radical of J
2) radical of radical of ideal I = radical of ideal I.</p>
<p>Please give me a detailed answer, I need it urgently!!!!</p>
<p>Thanks in advance!</p>
https://ask.sagemath.org/question/7990/ideal-radicals-question/?answer=12182#post-id-12182This is not a forum for homework questions. Your question has nothing to do with Sage.Sat, 12 Mar 2011 10:43:30 +0100https://ask.sagemath.org/question/7990/ideal-radicals-question/?answer=12182#post-id-12182Answer by kcrisman for <p>Hello experts,</p>
<p>Given that there is a commutative ring R and 2 ideals I and J, also given that I is included in J</p>
<p>I need to prove
1) radical of I is in radical of J
2) radical of radical of ideal I = radical of ideal I.</p>
<p>Please give me a detailed answer, I need it urgently!!!!</p>
<p>Thanks in advance!</p>
https://ask.sagemath.org/question/7990/ideal-radicals-question/?answer=12185#post-id-12185You may find [Math Stackexchange](http://math.stackexchange.com/) helpful. [Dr. Math](http://mathforum.org/dr/math/) also likely has something in their archives.
However, this forum is specifically for asking how to do things with [Sage](http://www.sagemath.org) 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](http://ask.sagemath.org/faq/) (which has a typo in one of the first lines... sigh).Sat, 12 Mar 2011 20:05:53 +0100https://ask.sagemath.org/question/7990/ideal-radicals-question/?answer=12185#post-id-12185Comment by niles for <p>You may find <a href="http://math.stackexchange.com/">Math Stackexchange</a> helpful. <a href="http://mathforum.org/dr/math/">Dr. Math</a> also likely has something in their archives.</p>
<p>However, this forum is specifically for asking how to do things with <a href="http://www.sagemath.org">Sage</a> mathematics software. We <em>can</em> compute radicals of ideals, which could conceivably help you gain intuition:</p>
<pre><code>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
</code></pre>
<p>However, using such forums for homework help is a breach of netiquette - see <a href="http://ask.sagemath.org/faq/">the FAQ</a> (which has a typo in one of the first lines... sigh).</p>
https://ask.sagemath.org/question/7990/ideal-radicals-question/?comment=22005#post-id-22005we 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"Sun, 13 Mar 2011 09:39:43 +0100https://ask.sagemath.org/question/7990/ideal-radicals-question/?comment=22005#post-id-22005Answer by Steve for <p>Hello experts,</p>
<p>Given that there is a commutative ring R and 2 ideals I and J, also given that I is included in J</p>
<p>I need to prove
1) radical of I is in radical of J
2) radical of radical of ideal I = radical of ideal I.</p>
<p>Please give me a detailed answer, I need it urgently!!!!</p>
<p>Thanks in advance!</p>
https://ask.sagemath.org/question/7990/ideal-radicals-question/?answer=12183#post-id-12183If 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?
Sat, 12 Mar 2011 10:56:13 +0100https://ask.sagemath.org/question/7990/ideal-radicals-question/?answer=12183#post-id-12183Comment by DSM for <p>If you know the answer just answer and if not please let others answer. I want to understand it that's all.</p>
<p>Why do you vote negatively for my question? You want me to vote for your questions and answers the same?</p>
https://ask.sagemath.org/question/7990/ideal-radicals-question/?comment=22006#post-id-22006Er, 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 math.stackexchange.com: 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..Sat, 12 Mar 2011 20:16:44 +0100https://ask.sagemath.org/question/7990/ideal-radicals-question/?comment=22006#post-id-22006Comment by John Palmieri for <p>If you know the answer just answer and if not please let others answer. I want to understand it that's all.</p>
<p>Why do you vote negatively for my question? You want me to vote for your questions and answers the same?</p>
https://ask.sagemath.org/question/7990/ideal-radicals-question/?comment=22007#post-id-22007If your question relates to Sage, it has a chance of getting answered here. If not, it won't. You could try asking at http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist;task=list.Sat, 12 Mar 2011 18:43:41 +0100https://ask.sagemath.org/question/7990/ideal-radicals-question/?comment=22007#post-id-22007