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January 6

abelian groups: dual group induces dual group of subgroup by restricting

Hello, let $G$ be an abelian group, with exponent e, meaning that e is the smallest positive integer, such that m times $g$ , for every $g\in G$ , equals zero.

Let ${\hat {G}}$ be the additive group of homomorphisms from $G$ to $\mathbb {Z} e$

If $H$ is a subgroup of $G$ , then restricting an element $f$ of ${\hat {G}}$ to $H$ , yields an element of ${\hat {H}}$ .

But do you really obtain all elements of ${\hat {H}}$ in this way? I guess so, but I don't think this is completely trivial?

I know that this is related to character theory, but I would love to see an argument without any use of complex numbers. Is that possible?

Kind regards,Evilbu (talk) 21:08, 6 January 2013 (UTC)[reply]

Problem with editting an article based on one's own published paper?

Hi.

I would like to ask a question about the title. As an amateur, I have somewhat succeeded in publishing my own article in the Journal of Mathematics Research (JMR), which is an open-access journal. I am quite not qualified for evaluating the quality of JMR, but when I go through Google looking for a special class of mathematical journals, I see some problems going on with qualities of those journals belonging to that class; according to some sites, some journals publish articles of any sort with payment, say even if it were written by computers.

Note that here I do NOT claim that the JMR is also one of them.

My question, then, is whether it is possible for me to edit an article (specificly, the article "Lindelof hypothesis") based on my article at the Journal of Mathematics Research. I heard from JMR that my article went through a peer-reviewing step, so I guess that my article should meet one of the rules of Wikipedia, and I myself of course have some trust on the validity of its contents. (I do know that Wikipedia is not a place to spread one's work. On the other hand, I perceive my result as quite an important contribution to the zeta-function theory, which should fall into the main object of this Wikipedia project.)

Apologies to you if you find my question to be somewhat arrogant.

Answers would be appreciated.

I guess maybe some rules with regard to this matter may be necessary anyway.

新谷の三男坊 (talk) 22:03, 6 January 2013 (UTC)[reply]

There are two parts to this. The first is whether or not JMR is regarded as a reliable source. If there is a question about this, the reliable sources noticeboard is the place to ask it. The second is whether you should be adding material derived only from your own published work. If it has been published in a reliable source then it is not original research, so that is not a concern; but you do have a slight conflict of interest, so it would be better to let other editors determine whether or not it is significant enough to be added to the article, by posting in the article's talk page. --ColinFine (talk) 22:12, 6 January 2013 (UTC)[reply]

I disagree with the statement that original research is not a problem. Indeed, this is precisely the sort of thing that the original research policy is supposed to prevent: a primary source, and one claiming to have a solution of the Lindelof hypothesis. For scientific discoveries, a general rule is that secondary sources must be used. (Also, the "Journal of Mathematics Research" is not a reliable source.) Sławomir Biały (talk) 01:41, 7 January 2013 (UTC)[reply]

There is some disagreement as to whether peer-reviewed journal articles are primary or secondary sources. --Trovatore (talk) 02:18, 7 January 2013 (UTC)[reply]

A peer-reviewed journal article can be a secondary source, but not for original results. I don't think there is any serious contention that a journal article can be used as a secondary source about its own results. The WP:V policy is also quite explicit on this, demanding third party souces that are independent of the subject being covered. Clearly a more liberal interpretation of these two policies opens the floodgates for all kinds of woo to get on Wikipedia (such as that under discussion). I'm aware that WP:IAR can be generously applied where there is a grey area, but this is not such a scenario. Sławomir Biały (talk) 13:22, 7 January 2013 (UTC)[reply]

Then, I should not edit based on my own article because of various reasons. Thanks for your opinions.新谷の三男坊 (talk) 22:06, 8 January 2013 (UTC)[reply]

By the way, what happens if a guy, who is not a friend of mine, publishes a research paper in a different journal belonging to that special class of jounrals citing my article, by chance? In the least, that would satisfy the third party condition of Wikipedia.

In general, I think it is unfair to ignore that special class of jounrals only because of its accordingly poor peer-reviewing process.

Why don't we make Math Wikipedia different and newer from mathematical societies? Wikipedia, in my thought, should be a kind of groups which is _active_ to search for new results such as journalists, rather than which _waits_ for appearance of new results (such as researchers at universities). While mathematical societies are just mathematics, Wikipedia should be rather Mathematics times Journalism, shouldn't it? And what do journalists do in general? Of course they try to spread truth, but they do not ignore possibly interesting events.

Again, apologies to those if the last comment were taken as some sort of insults towards academicians. But I somewhat feel that academicians, especially mathematicians, wait for a result to be validated by many people until one particular mathematician agrees on it.

Or, this strong belief of mine might die off the moment my article at JMR were proven to be wrong by some generous professionalists. [The link by Trovatore is precisely my article.]

Any comments would be greatly appreciated.新谷の三男坊 (talk) 21:55, 9 January 2013 (UTC)[reply]

I'm not sure what you mean by the link I posted. I don't think I posted a link, except to my own user and user-talk pages.

On the substance, it's fine to argue that there should be such a thing (actually I think there is such a thing — have you checked out MathOverflow?) but it isn't Wikipedia. Wikipedia is an encyclopedia, which is an extremely conservative form, by nature and design. --Trovatore (talk) 22:03, 9 January 2013 (UTC)[reply]

Well, it is precisely a "poor peer-reviewing process" that makes a source generally unsuitable. Wikipedia is an encyclopedia, the aim has always been that it "_waits_ for appearance of new results" in any area, not to be original. On the other hand, if an article has been published in a respected journal, like the Annals of Mathematics or Crelle's Journal, that is quite sufficient for the article to be considered as a source for its own results. That is the consensus at WP:RSN. That is the intent of the rules and common practice, imho anything else would be unworkable. So no, there is no absolute problem with editing an article based on your own published paper. What counts is where it was published or how it was received by recognized experts.John Z (talk) 22:19, 9 January 2013 (UTC)[reply]

That seems to be contrary to what Sławomir said above, John. --ColinFine (talk) 07:38, 10 January 2013 (UTC)[reply]

Thanks John, for your comments. There already is an absolute rule for what I have been arguing about, then. I would say no more. I might try MathOverflow, and hope that I could come back to Wikipedia with something new to add. 新谷の三男坊 (talk) 21:30, 10 January 2013 (UTC)[reply]