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I provided an answer (whether it really is one or not is a matter of dispute) to the following question: Where does the proof for commutative rings break down in the non-commutative ring when showing only two ideals implies the ring is a field?

My answer was deleted on the grounds that it does not answer the question. So far so good. Now how come that there is another "answer" (the one with the Weyl algebra) which also does not answer the question (which is "where does the proof for commutative rings break down in the non-commutative ring?"). In fact it is rather obvious that my answer (or comment or whatever) is certainly more relevant than the one with the Weyl algebra. (If people disagree here, I recommend to understand the question properly, it did not ask for a counterexample or whatever, but WHERE DOES THE PROOF BREAK DOWN. Actually none of the answers really answers the question, which is also obvious.)

So how can this most obvious unequal treatment be explained? Is it because the guy that deleted my answer is a friend of the other one or is it because he believes in "reputation" (which is a misnomer at any rate)? I should say that this is not so much about this particular question, but a matter of principle. It is clear that there are many other cases.

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    $\begingroup$ I have some sympathy for your cause, but I think that slade's answer does address the original question. Did you see the comment "This would be a highly relevant comment to the original post, but it's out of place in the solutions.." under your post? IMO also your post is very relevant, but it does not look like an answer, a hint may be, if you mark it as such. I am sure that the handling moderator was not playing favorites. Observe that the answer with Weyl algebras has not received any upvotes (justifiably so). Apparently nobody has flagged that answer yet. $\endgroup$ – Jyrki Lahtonen Dec 20 '14 at 12:48
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    $\begingroup$ @JyrkiLahtonen: I think he means the other answer. Not that this other answer was posted after the edit. And this answer makes good sense given the question in the title. Also, I don't think a moderator would delete a wrong answer. $\endgroup$ – Thomas Dec 20 '14 at 14:23
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    $\begingroup$ 313: If you believe that an answer is wrong you could write a comment below the answer. If you don't get a response after some time, you could even downvote... $\endgroup$ – Thomas Dec 20 '14 at 14:24
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    $\begingroup$ @313: Again, you could also try and leave a nice comment below the answer explaining why you believe it is a wrong answer. I don't think you received unequal treatment. A moderator shouldn't delete a wrong answer. $\endgroup$ – Thomas Dec 20 '14 at 14:42
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    $\begingroup$ @313: Ahh... maybe the problem is in the definition of an answer then. Note, by the way, that this other answer was given after the edit. The edit changed the title and given the question in the title, the other answer actually makes sense. So maybe we can agree that this is all probably just due to a bad edit? $\endgroup$ – Thomas Dec 20 '14 at 14:48
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    $\begingroup$ @313: Also, did you actually try to flag the other answer? $\endgroup$ – Thomas Dec 20 '14 at 14:50
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    $\begingroup$ @Thomas: As 313 specificies that the other answer mentioning Weyl algebras, it is clear that they suspect Pedro's answer getting preferential treatment over theirs. Pedro has edited his counterexample to an answer since, and has climbed back to 0 from -1. Effectively 313 has been denied a similar opportunity to upgrade his comment/hint (voted +3 at the time of deletion) to an answer/hint. So I understand why they are miffed. But I don't suspect foul play. I'm not fully certain myself, where the line between a comment/hint/answer is. A moderator made a judgement call. $\endgroup$ – Jyrki Lahtonen Dec 20 '14 at 20:32
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    $\begingroup$ For comparison take a look at one of the answers by yours truly. I think of it as a pithy one-liner myself, but IIRC somebody has flagged it as unhelpful or some such. You be the judge! Hints are a bit delicate, and to be acceptable as answers, need to be convincing to those who know. I think 313 should have A) marked this at a hint, and B) made it a bit more convincing. As it was written it is not entirely convincing even though it is possible that 313 in their heart was satisfied with it though. $\endgroup$ – Jyrki Lahtonen Dec 20 '14 at 20:43
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    $\begingroup$ (cont'd) If they had added a sentence like: A principal one-sided ideal contains only multiples of the generator, I would not have converted it to a comment, because then it would have been convincing. I would have upvoted it instead. So.... Welcome to the club of hint-answerers, 313! It is a somewhat tricky businedd, and this time it unfortunately backfired. Better luck next time! $\endgroup$ – Jyrki Lahtonen Dec 20 '14 at 20:47
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    $\begingroup$ @JyrkiLahtonen: Sorry. I misunderstood your first comment. I thought that you thought that the "other" answer was slade's answer. Hopefully you will now think that I thought that you thought what everyone else thought ... or something like that :) $\endgroup$ – Thomas Dec 20 '14 at 20:57
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    $\begingroup$ @JyrkiLahtonen I think calling this a hint is being very charitable. To all appearances, it is not much different from "Did you mean "for all nonzero $x$?" or "This question doesn't make much sense as it is, you should..." It seems to be entirely about improvement of the statement of the question. If it can be interpreted as a hint-answer, it is a very oblique hint. $\endgroup$ – rschwieb Dec 21 '14 at 14:01
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    $\begingroup$ That's basically why I left the comment I left, anyhow, and probably what the moderator was thinking too. I fully expect, though, that @313 will be able to make clearer hint-answers after this discussion, so I'll be on the lookout for those next time around (in a positive way, not because I'm intend to criticize them :) ) $\endgroup$ – rschwieb Dec 21 '14 at 14:09
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    $\begingroup$ @rschwieb: Understood. Undoubtedly you noticed that I never said I disagreed with mod's decision. Admittedly at the moment I'm so "enchanted" with the possibility of giving 313 a chance to fix the comment/answer. I haven't thought about the ramifications of such a policy yet. I also don't know how many flags there were on 313's post. $\endgroup$ – Jyrki Lahtonen Dec 21 '14 at 15:37
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    $\begingroup$ What is the "answer" in question, really this? "In a noncommutative ring you have to distinguish between left, right, and two-sided ideals. So you first have to take care of this. What do you even mean by a maximal ideal in a noncommutative ring? Do you take it to be left, right,... ideal?" It is clearly NAA. $\endgroup$ – quid Dec 22 '14 at 1:11
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    $\begingroup$ @313 "Also by intelligence it is now known to me that Pedro Tamaroff flagged my post." In that case, intelligence can apparently not be trusted. I checked who flagged your answer. $\endgroup$ – Michael Greinecker Dec 22 '14 at 13:49
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The meaning of "not an answer" can be somewhat counter-intuitive and thus sometimes leads to confusions.

Text written in the answer box should be flagged as not an answer when "[it] was posted as an answer, but it does not attempt to answer the question. It should possibly be an edit, a comment, another question, or deleted altogether."

Put differently, text written in the answer-box attempting to answer the question (yet failing to do so) should not be flagged as NAA. It could be commented on, be down-voted, and in extreme cases be flagged as "very low quality" or voted to delete.

Whether something is "not an answer" (in this technical sense) is rather based on criteria of form.

In view of the above it is in my opinion not surprising why the one answer was considered "not an answer" and converted to a comment, while the other was not.

In a noncommutative ring you have to distinguish between left, right, and two-sided ideals. So you first have to take care of this. What do you even mean by a maximal ideal in a noncommutative ring? Do you take it to be left, right,... ideal?

This text is, or at least looks like, commentary on the post and not a (direct) attempt to answer the question, at least not in a formal sense. If the idea was to encourage the OP to think about this and to inspect the proofs keeping this in mind as it would lead them to a resolution of their problem (which might qualify as an answer), this should be made clear.

By contrast the other text in an answer box was:

For a counterexample take the first Weyl algebra $\mathbf C[p,q]$ where $pq-qp=1$.

This clearly attempts to answer the question. Whether it is wrong, or answers the wrong question or is bad in some other way is irrelevant for deciding if it is "not an answer." [I do not claim this was the case, neither the contrary, it is for the sake of argument.] It is manifestly an attempt at an answer; the merits of which are judged via mainly up/down-voting and in rare cases via "low quality" flags (and deletion), yet not via "not an answer" flags.

This distinction might seem a bit bureaucratic, yet on an ever larger site some structuring is needed.

To sum this up: text in the answer-box should be clearly recognizable as an (attempt to) answer even without engaging in detail with the content or context in detail. Then it is save from conversion to a comment as "not an answer." (It might still be deleted for other reasons, in extreme cases.)

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  • $\begingroup$ What I am saying is that the text your wrote seems (at least at first glance) like a (good) comment requesting clarification and not like an (attempt to) answer. To repeat: the NAA-flag is almost exclusively there to signal that a user does not use the site in the way it is intended on a technical level; there are other ways such as downvotes, the LQ-flag, direct votes to delete, to deal with users that use the site as intended but post bad content. $\endgroup$ – quid Dec 22 '14 at 21:05
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    $\begingroup$ The main issue, let me stress this again, is that does 'not answer the question' is used in different ways. I agree that PT's text was not a valid answer to the question, however it was an attempt, therefore it should not be flagged as NAA, yet one might nevertheless think it should be deleted (but the threshold is bit higher for this type of deletion, since after all in your case only a conversion happened). I do not understand your final misgiving about my answer. $\endgroup$ – quid Dec 22 '14 at 21:05
  • $\begingroup$ Let me repeat with emphasis what I wrote: 'the merits of which are judged via mainly up/down-voting and in rare cases via "low quality" flags (and deletion), yet not via "not an answer" flags.' It is perfectly possible that an attempt to answer that turns out not to be a valid answer gets deleted; yet still it should not be flagged as NAA. $\endgroup$ – quid Dec 22 '14 at 21:06
  • $\begingroup$ If you do not believe me, perhaps you believe the description built into the software that I quoted for you, here it is again: "This was posted as an answer, but it does not attempt to answer the question. It should possibly be an edit, a comment, another question, or deleted altogether." Please pay special attention to the word "attempt." You are free to consider the NAA as a useless or misguided design. But it is there for what I said it is there, and if you want to get the best results on this site it can help to use the tools in the way they are intended. $\endgroup$ – quid Dec 22 '14 at 21:10
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    $\begingroup$ The problem that this flag tries to solve is that many users do not use the site properly. They will post "I am interested in this problem too." "This is so interesting." "This is boring." "Can you please clarify this." "I would have this follow up question." And so on all as answers since they are used to discussion boards, or do not find another box where to type and so on. This is so frequent that a specific tool was created to deal with this that unfortunately has a confusing name, the NAA flag. (There are debates to rename it even.) You triggered it, via seeming to ask clarification. $\endgroup$ – quid Dec 22 '14 at 22:20
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I think answers that are considered low quality and not an answer needs to be thoroughly addressed. There is a meta post floating around about hints being an answer but they are constantly flagged as low quality any ways. I have noticed that posts that are as long as hints but don't contain the word Hint in bold font tend to be deleted more often then hints with two words. I don't think a two or three word hints should be an answer but that is besides the point. If those are acceptable any short post that answers (I use answer loosely) should be acceptable then as long as the tempt isn't spam or nonsense. If said answer gets down voted, oh well.

Let me expand. If the community is willing to accept an answer that consists of two three words as appropriate, an answer that attempts to answer the question shouldn't be low quality or not an answer even if it is wrong. Not all answers are correct. By definition, an answer is a reply to a question; that is, correctness isn't consider. If someone has a good faith attempt to answer, it is credible even it is wrong. If it is wrong, let the voters decided but do not have it removed or moved to a comment by anyone but the poster. How can we justify this when we accept Hint: quadratic equation (example have no clue if this was used any where)?

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    $\begingroup$ @313 you dont understand the definition spam if that is what you think. I believe your answer shouldnt have been deleted but your response makes me want to reconsider having your back. $\endgroup$ – dustin Dec 20 '14 at 19:44
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    $\begingroup$ @313 No flagging determines spam. See for yourself $\endgroup$ – dustin Dec 21 '14 at 0:55
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    $\begingroup$ @313 "Spam" is a carefully defined term that refers to a particular type of post. A post with which people disagree (and therefore downvote) is not spam. I encourage you to do some research here on meta about what counts as spam what does not. $\endgroup$ – apnorton Dec 21 '14 at 5:36
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    $\begingroup$ @313 you asking a question solicites responses; that is, it isnt unsolicited. You really need to understand the words you use because they are entirely incorrect. $\endgroup$ – dustin Dec 21 '14 at 16:41
  • $\begingroup$ @313 you dont have a lot of understanding of voting on meta. You should take anorton suggestion and do some reading since you seem very confused. $\endgroup$ – dustin Dec 21 '14 at 19:38

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