When I was undergraduate I proved something which was non trivial (but I have to be honest, it was not something very important) in mathematics and i presented it to a professor at the university. He found it correct and he included the theorem in his new book (it was new - this happened in 2008) with my name along the theorem. Now you can find this theorem in another book published from Springer.

  1. I was wondering if this is considered as one of my own publications.
  2. If I submit it to a journal, should I mention the situation with the books?
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    I think the question is: can I publish it again in a Journal? And the answer is: it depends on the journal, but most likely not unless there is some additional new contribution to the previous work. – Trylks Nov 20 '14 at 11:21
  • @Trylks On the other hand, you get extended abstracts in conferences transformed to full papers published in a journal very often, and it seems fine to everybody. But as you say: the journal can do as they wish. – yo' Nov 20 '14 at 11:34
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    When you say "considered as a publication", do you mean "Is the theorem considered to be published" or do you mean "Can I count this as one of my own publications"? – Oswald Veblen Nov 20 '14 at 12:01
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    @OswaldVeblen the second question is what I am asking. – Konstantinos Gaitanas Nov 20 '14 at 13:57

First, you should take pride in proving a theorem that was significant enough for someone to attach your name to it. Even if it was "not very important", as you say, it was still enough to be worth mentioning. Not many undergraduates achieve that.

When you submit to a journal, you don't submit a theorem, of course -- you submit a complete paper. A typical paper has more than one theorem, unless the one theorem is particularly good. In this case, if you describe your theorem as nontrivial but "not very important", it seems unlikely to make a paper on its own.

If you write a paper, you could certainly include the theorem in question. Because the original book attributes the theorem to you, everyone knows it's your theorem, so there is no issue with 'stealing credit'. In the paper, you could say something like

The following theorem has appeared in Smith [1, Theorem 4.5].

just before you state and prove the theorem. This sort of thing is routine, and as long as the theorem fits nicely into the paper it is unlikely that the referee will complain. To answer part of the question, you should mention that the theorem has appeared in the book already.

At the same time, you will need to make sure that the new content of the paper is enough to merit publication (that is, the previously unpublished results that you put in your paper). As you read more papers in your area, you will get a better sense of how this works in practice.

I think you have also asked whether you can include the book in your vita. The answer is no. But at various times you are asked to write a research statement or research narrative. Because the book attributes the theorem to you, you can state and take credit for the theorem in your research statement. This is particularly relevant if you are applying to graduate schools.

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    +1 This really sounds like something the OP should be more proud of. – xLeitix Nov 20 '14 at 13:17
  • Thank you very much for the responce. I upvoted every answer since they are very usefull but I cannot resist to thank you 15 times more. – Konstantinos Gaitanas Nov 20 '14 at 13:59
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    @KonstantinosGaitanas - you are a (budding) mathematician, so you should realize you are thanking Oswald "1.5 times more" than the others...?!! – Floris Nov 20 '14 at 19:32
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    @Floris yes I reallized this later but I am sure that everyone undesrtands what I mean! – Konstantinos Gaitanas Nov 20 '14 at 19:45
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    "The following theorem has appeared in Smith [1, Theorem 4.5]." Stated like this, I would never imagine that the theorem had been first proved by the OP. Especially if, as you write it, the proof of the theorem follows, I will not bother looking at the book by Smith (do I own it? Is there at the library?), and assume the OP put it in the paper for the sake of completeness. Is it too much to write in a paper something like "The following theorem had been first proved by the author as a contribution (Theorem 4.5) to [Smith]" ? I think this emphasizes the OP is the original author of the proof. – Taladris Nov 22 '14 at 4:18
  1. I was wondering if this is considered as a publication.

Yes this is a published work and can be referenced by other publications. You are not the author of the published work in this particular case.

  1. If I submit it to a journal, should I mention the situation with the books?

Yes it should form a part of your bibliography / references or some other citation within the paper as it is relevant

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    How can a book by person A be part of the publication list for person B? – Oswald Veblen Nov 20 '14 at 12:00
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    I wasn't implying that it could – Kaido Nov 20 '14 at 14:28
  • I am not sure what someone's "bibliography/references" would be, apart from their list of publications - could you expand or clarify the answer to explain that? – Oswald Veblen Nov 20 '14 at 17:44
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    "My own publications" generally means "publications by me, for which I receive credit and which I include in the publication list for myself". So by saying "yes" to the first question, you very much imply that the book should be part of the publication list for the questioner. However, I don't think that's what you intended to imply. I think you just intended to say that it can be referenced from the questioner's future publications, but answering "yes" to 1. is a confusing way to do that. – Steve Jessop Nov 21 '14 at 12:30
  • Thanks - Question had changed between my answering and editing, altering the context of my answer. I've updated for clarity. – Kaido Nov 21 '14 at 12:59

If you ask whether the theorem is considered as published, then the answer is yes, it is, and it can be cited from either of the two sources you know.

If you ask whether it can be considered as your publication, then the answer is no, it cannot. Proving a theorem and having a publication are two different things. It is just a bit strange that the professor published it in his book without your consent (or have he asked you beforehand?), as a matter of politeness, I would consider it better if he asked you beforehand. You could have asked him to list you as a co-author for instance of the chapter in the book; then you could list the chapter as your publication.

I would be very careful about submitting it to a journal, since it is obviously a previously published work. It probably can be treated similarly as a conference extended abstract re-published as a full paper so you may be fine, but the journal may as well decide to reject the publication as "not containing original work"/"previously published". Certainly, however, you can publish it on arXiv or similar repositories; this is not a full publication, but it can be cited and included in your list of publications.

Originally, I said that it was unprofessional from the professor. After the comment by Oswald Veblen, I realized that it's really not so uncommon.

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    I don't see it as unprofessional to include a relevant and interesting theorem in a book with an attribution to the person who proved it, even though the theorem is not otherwise published. This happens all the time. – Oswald Veblen Nov 20 '14 at 11:59
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    The whole concept of extending conference abstracts to full papers is not really used in mathematics, so I don't see how it would be applied here. – Tobias Kildetoft Nov 20 '14 at 12:25
  • @TobiasKildetoft Probably depends on which part of mathematics you are in. I'm on the boundary of maths and TCS, and we do that all the time. – yo' Nov 20 '14 at 12:40

I see that you have published a paper in the arxiv. You could certainly write up your theorem, optionally with background and/or example(s), and submit it. That is certainly a common thing to include in a publication list.

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