This question has been put on hold although it is very precisely formulated and evokes an interesting and underestimated property of rings.
The question is intimately related to a useful concept in scheme theory: the maximal points (introduced in Grothendieck and Dieudonné's EGA), which generalize the non always present generic point of a scheme.
There is no proof that the question is homework, although this is taken for granted in the explanation for the on-holding it.
The OP's imperative tone ("show that...") is a little rough, but we are mathematicians, not thin-skinned aristocrats at the court of Louis XIV, and we should not let this seriously bother us .
Finally, that someone has no activity in or knowledge of a topic does not mean that a related question should be called off-topic.
I have voted to reopen the question and would like to reemphasize how idiotic and nefarious is the (out of our control, I know) rule that five persons with absolutely no proven competence in a subject can on-hold a question on a site with about 65000 registered users.

Edit
Sadly the answer and comments to my question are in the same vein as the reasons of the onholders : they consist in general formal statements on how a question should be formulated and on the fact that I'm ranting. Yes, I am ranting because the question should not have been put on hold.
There is zero consideration for the mathematics involved, which is strange on a mathematical site which is not officially a site on étiquette.

To repeat: rings with just one prime ideal are interesting and useful in algebraic geometry. The OP asks why they are the same as rings whose nilradical is a prime. This is a good question, exactly at the level of this site. My ranting question: is there a mathematical argument for putting it on hold ?

New Edit
The question has just been reopened. Thanks to all the reopeners (with one obvious exception).

Even newer but hopefully last edit
I have had three downvotes on main today , which is the record in the 34 months I heve been registered on math.stackexchange (but the day is not over yet...).
One of them was for this answer which had had 21 upvotes and no other downvote since it was posted on the 21st of March 2012.
I don't think that this downvote, nor the others, are independent of this discussion.
I don't really care so much about reputation (although being a human being, I confess it has a certain vanity appeal) but that kind of behaviour considerably cools my desire for any further discussion here and I will now go back to my dear geometry on main, enjoy the great questions and answers there and try to contribute if I can.

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If we cut the rant ("thin-skinned aristocrats", "idiotic", "nefarious", "no proven competence"), this could have been an answer to this meta question. –  Lord_Farin Sep 11 '13 at 22:15
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Indeed, this was quite the rant. –  mixedmath Sep 11 '13 at 22:18
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Whether it's a good policy for PSQs to be closed on sight has come up on meta a number of times, and (IMO unfortunately) the tide of opinion seems to be in factor of more closures. My impression is that this is held in favor partly to optimize for sand and not pearls, as mixedmath says, and partly to be punitive to people who don't think (or know) to format their questions how others want them to. Indeed, good questions will be closed by people who do not understand their significance probably for this reason. –  anon Sep 12 '13 at 0:20
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@anon: what is PSQ ? –  Georges Elencwajg Sep 12 '13 at 0:22
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It would be ideal if the poster included more one just one sentence, but I also think the question is mathematically interesting. Also, since Georges is an expert in commutative algebra/algebraic geometry, I think it makes sense that his opinion on closure for this question should weigh more. Just look at the his mostly voted tags from his user page! It would be interesting if only those users with sufficient reputation points on a certain tag [X] were able to cast a vote to close a question tagged [X]. This would essentially solve the problem addressed just above the word Edit above. –  Prism Sep 12 '13 at 0:30
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@anon: I don't think punishing questioners for formatting reasons is a good idea and, more importantly, the punished people in this case will be all the users prevented from participation in a thread about quasi-fields. –  Georges Elencwajg Sep 12 '13 at 0:32
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Thanks, @Prism. I had not thought of your extremely ingenious idea of restricting closing votes to people with sufficient reputation on the tag of the question: this would indeed very elegantly solve most of the problem. –  Georges Elencwajg Sep 12 '13 at 0:39
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I also don't like the idea of being punitive for not respective community etiquette. Closing a question because of formatting even when a question itself is good mathematically and otherwise beneficial to have seems heavyhanded, alienating and insincere. I think users should be more stringent in how they close vote, choosing to let others do the voting when they are not completely sure and confident an individual question deserves and would be better of closed. –  anon Sep 12 '13 at 0:42
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By the way PSQ = problem statement question. –  anon Sep 12 '13 at 0:52
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@GeorgesElencwajg: You are welcome! Thank you for your excellent contributions here. Your answers have always enlightened me, and helped me to enhance my understanding of commutative algebra. And also thank you for treating all the users here in such gentle manner. –  Prism Sep 12 '13 at 0:59
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@anon ("good questions will be closed by people who do not understand their significance"): "good" is contextual. The anti-PSQ contention is that a question which makes a good exercise in a textbook is not, in general, a good question for MSE without additional information to tell the answerers which results they can assume the asker to know (or to be supposed to know, at least). –  Peter Taylor Sep 12 '13 at 7:40
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@GeorgesElencwajg: You're getting general formal statements because you effectively make attacks on the very idea of closing, rather than limiting yourself to reasons why this question should be the exception. Also, I think "I like the topic" is almost completely irrelevant to whether a question should be an exception. –  Hurkyl Sep 12 '13 at 12:40
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... more precisely, liking a topic does nothing to mitigate the reasons why a question should be closed. Any merit in such a thing lies entirely in serving as a bribe to attract/keep specific people who like to answer such questions (even ones that should be closed). Personally, I despise that sort of thing. –  Hurkyl Sep 12 '13 at 12:52
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Downvoting just for meta disagreements is appalling. –  Asaf Karagila Sep 12 '13 at 19:49
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@GeorgesElencwajg: I don't know if whoever is making these votes is actually a mathematician. –  Asaf Karagila Sep 13 '13 at 6:53
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5 Answers

While I do support that to some extent people shouldn't vote to close questions in topics they are less familiar with, I also think that the question (as originally posed) should have been closed.

The reason is that bad questions breed bad questions. I don't like questions which seem copy-pasted questions when I encounter them in logic and set theory tags. Sometimes I will answer them, and sometimes I won't; sometimes I will vote up, down or to close and perhaps even delete later on, and sometimes I won't.

The problem with questions that seem like copy-pasta texts is that on occasion users actually look at some arbitrary questions and answers, before posting their own, in order to see how the standards are. I don't want those rare users to get the impression that it's okay to copy-paste from some text, just because "they good folks of algebraic geometry are tolerant to all questions".

In light of that I will do my best to continue voting against questions which the author revealed absolutely nothing about their thoughts regarding the problem. If anyone finds this method problematic, they are free to edit the questions before they are closed, I will be happy to retract my vote (which is now possible) or vote to reopen if an expert wants to post an answer but can't.

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For instance, this question seems to fit closing criterion, right ? –  Cantlog Sep 12 '13 at 23:05
    
That's borderline. –  Asaf Karagila Sep 13 '13 at 5:12
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I did not put the question on hold, but I support it being on hold. The phrase "homework questions" in the reason to close should really say "any question."

The fact is that the OP was nothing more than a problem statement and a demand for a solution. There is no work, no motivation, no attempt, no "research effort," and no source.

At the end of the day, I want to optimize for pearls, not sand, so it does not bother me at all the users feel inclined to close such questions.

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+1. I have on more than one occasion used a custom close reason referencing the How to ask a homework question thread on the basis that the principles there apply to all questions. –  Peter Taylor Sep 11 '13 at 22:20
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Oh, I certainly believe you when you say that you are not bothered at all by the closing of this question. Do you have any interest or knowledge in algebraic geometry? Would you have solved the question if the OP had shown "work,motivation, attempt, research effort, source " ? –  Georges Elencwajg Sep 11 '13 at 22:41
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While closing PSQs as a matter of policy will mostly only target mild-interest homework-level questions, it will inevitably from time to time target mathematically good questions that the site and our readers would benefit from having. In other words, broad interpretation and reflexive application of a PSQ closure policy will in fact lead to collateral damage wherein pearls are discarded as if they were sand (mitigated slightly by closures being case-by-case). Citing the reasons for having a PSQ policy without addressing whether this particular question is collateral damage seems disingenuous. –  anon Sep 12 '13 at 0:13
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@GeorgesElencwajg I second mixedmath on this, and would like to add: putting questions on-hold is not permanent. If you don't think a question should be on hold, you can vote to reopen. If the question is improved (as it hopefully will be), vote to reopen and post it in the thread specifically for soliciting reopen votes. These are much more constructive than posting a rant on meta. –  Alex Becker Sep 12 '13 at 1:06
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@Alex: yes I know, I had already voted to reopen. You may be right about the constructiveness of rants, but human beings, even algebraic geometers, are subject to emotions and... But this will be a subject for psychology.stackexchange (if it exists) :-) –  Georges Elencwajg Sep 12 '13 at 1:23
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@Georges: I do not understand why you disparage my algebraic geometry. Yes I know algebraic geometry, yes I could have answered his question. I also do not know why you disparage Alex Becker, or the other mods, or other mathematicians in general. And I do not understand your 'woe to algebraic geometers' bit in your comments here. If you are insinuating something, it is currently lost on me. –  mixedmath Sep 12 '13 at 2:45
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@GeorgesElencwajg You seem to be missing the reason questions like these are closed. It is not that the question itself is not mathematically interesting. It is that if the OP just gets a full solution, that is unlikely to be as helpful to them as getting hints that allow them to solve it themselves (and even though it might not be homework, it is clearly an exercise from somewhere). For example, I left a comment asking if they could at least prove one of the directions (one of them being slightly easier than the other), but before they had a chance to respond, a full answer had been given. –  Tobias Kildetoft Sep 12 '13 at 6:46
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@mixedmath: I didn't "disparage [your] algebraic geometry" nor anybody elses's, but asked you two questions of which you answered the first (the second asked if you would have answered his question, not if you could have answered it). I am happy that you know algebraic geometry and I hope you will let this site profit from your knowledge by answering the questions with that tag which satisfy your criteria of showing "work, motivation, attempt, "research effort", and source". –  Georges Elencwajg Sep 12 '13 at 7:26
    
Dear @Tobias: your point of view is eminently respectable and I am glad you expressed it. There is, however, a huge difference between criticizing a question (which is quite legitimate) and putting it on hold, which I disapprove of in the present case. –  Georges Elencwajg Sep 12 '13 at 7:48
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@GeorgesElencwajg Putting the question on hold is the only way to prevent people from answering it until the OP has had a chance to give people an idea of precisely what hints will be the best for him/her. That the question already had several answers when it was put on hold makes this reason moot of course, so I would probably not have voted to close myself. –  Tobias Kildetoft Sep 12 '13 at 7:55
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@Tobias: It is interesting to put on hold a question that's already been answered. I suppose perhaps users are optimistic and think that it will then serve as an indication to the rest of the community, saying 'these questions aren't welcome.' I don't know, just speculation. –  mixedmath Sep 12 '13 at 10:52
    
physics.stackexchange.com/questions/76561/… this link will show you my question on physics.stackexchange. It says that you haven't put a great effort into this question so we close it. I had derived an answer so, how much more effort could i put into it. Secondly, it wasn't a homework question. It was just a random question which i had in mind –  Rafique Sep 12 '13 at 19:44
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@Muhammad: I don't understand. Are you asking a question about Physics.SE on the math meta? This is not the appropriate place for that community. You should go to the physics meta instead. –  mixedmath Sep 12 '13 at 22:04
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In this case there were close votes that would have prevented the pearl, and close votes after the pearl answer was posted. This is not "optimizing for pearls", but enforcing a house style on questions as an end in itself. –  zyx Sep 14 '13 at 19:48
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There are excellent questions, and then there are excellent questions. A truly excellent question is wonderful both because it has deep mathematical content and because it has exceptional prose. Questioners cannot be expected to achieve both of those in every question, but we can expect some level of mathematical interest (otherwise, the question is off-topic or too narrow) and some level of prose quality.

The same is true, of course, for "mathematical proofs". Some tolerate a proof that has the "right idea" even if it it written in awful prose and contains slight errors. Others feel that a proof needs to be written carefully, with correct prose, in order to truly be a proof.

The question under discussion has some mathematical interest, although as the answers show it is really just an exercise, and many people will recognize it as such. On the other hand, the prose is bad, and was originally worse. When the question was posed ( link ) it was a bare demand for a proof, with the same appearance it would have on a list of homework problems. The asker has very low rep, as a new user would.

What would have been nice is a comment on the question explaining to the asker how they could improve the question (e.g. by explaining what they had tried already). The closure boilerplate text is not very good at describing that. But in the end it is up to the asker to meet community standards, and if you look at the questions posed by high-rep users, they go well beyond a verbatim copy of a standard homework exercise.

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+1, especially for the last paragraph. –  Cantlog Sep 12 '13 at 21:06
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I have voted both for closing and reopening. Let's explain my motivation:

I think there is some dilemma. On the one hand, we get dozens of standard questions hastily copied from exercise sheets, without any own effort. Sometimes they come with the (homework) tag, more often they don't. I think it is important to counter this behaviour in some way, to keep the quality and attractiveness of math.SE at a reasonable level. It's hard to tell if the current mechanism of putting them on hold is the best approach, but — no matter if you like it or not — this is the status quo at the moment. For me, the question under discussion looks like a typical literal copy of an exercise (admittedly not from a freshman lecture).

That was the reason for me to opt for closing it in the first place.

On the other hand, there is the danger to close interesting questions, only because they are stated in a mathematical precise way without any garnishment. To give another example: I find this question quite interesting, but I can't blame the 5 persons for closing it. I think a good way to deal with this situation is to nominate the question for reopening or to put a request here, and to make clear that the question is interesting not only for the OP, for example by adding a comment or editing a note into the question.

That was the reason for me to opt for re-opening the question after reading your post.

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+1 for a well-balanced consideration of policy quality! –  Lord_Farin Sep 12 '13 at 11:58
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More of an announcement than anything else:

I have decided to temporarily lock the question under discussion. The question has now gone through three complete close/re-open cycles, in large part due (in my opinion) to this very thread. The question itself seems to have become symbolic to both sides of the so-called PSQ debate, and (again, in my opinion) the ongoing close/re-open war is not the proper way to express one's opinion in this debate. I hope that its being locked shifts the focus of this debate away from this specific question.

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Thank you. I do wonder sometimes whether users should avoid closing a question they would otherwise vote to close, merely because they encountered the question via a meta thread. So far, I have taken the opinion that this phenomenon is just an example of the Streisand effect: if a poor quality question is advertised on meta, more people will notice it, and vote to close it not out of any sort of spite but because they habitually vote to close that type of question. –  Carl Mummert Sep 13 '13 at 13:49
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After roughly how long do you think you'll unlock the question? –  Isaac Sep 14 '13 at 17:33
    
The tide of votes on this question and the one it references in MSE has been slightly in favor of opening, and this is even more so if @CarlMummert 's comment is correct. That is, the vote counts, already positive in total, are a false-negative about the natural opinion levels on the question had the thread not been posted. I do not think the MSE question would be re-closed, or that there would be more close-reopen rounds, without specific campaigning in meta against the question. Locking is more of a self-fulfilling prophecy that redefines a kerfuffle into a war. –  zyx Sep 14 '13 at 19:55
    
Unlocked 4 days later. @Isaac –  zyx Sep 23 '13 at 21:06
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