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I work in the field of algebra (more specifically the representation theory of groups). I published most of my papers in journals of algebra and another algebra journal of similar quality as journal of algebra and think about having some papers now in slightly better journals. (It would be good if the editorial board has some names close to my field of research, but this is optional.) Here are some examples that come to my mind: Mathematische Zeitschrift, the Journals of the London mathematical society, IMRN.

  • Is it considered to be much better to have a publication in such a general journal than in a specialized journal like Journal of Algebra? I made the experience that sending my papers to Journal of Algebra, one gets a much quicker publication and the editors are closer to my field. So from my side I would just send all my papers to Journal of Algebra or another specialised journal, but I assume that this will look weird in my CV. Does it harm me if I do this even when some of my papers could go into a slightly better journal like Mathematische Zeitschrift? I feel uncomfortable sending my papers to editors that are far away from my field of research.

Some secondary questions:

  • How bad is it to have a very good paper (that might be suitable for the best general journals) published in a journal like Journal of Algebra?

  • Can one give an approximate how much worth a paper in Advances of Math (or a similar or better journal) is compared to a paper in journal of algebra? Like 3 Journal of Algebra papers = one Advances of Math paper and 6 Journal of Algebra papers = 1 Inventiones paper?

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    I think it is a legitimate question. Actually, one of the most on topic and legitimate questions an academic can ask. – Dilworth Oct 5 '17 at 11:56
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    Probably not even a partial answer to your first question: The Australian Mathematical Society ranks the Journal of Algebra among the best journals. – Christian Oct 5 '17 at 12:00
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    @Christian Unfortunately, that list is outdated by now. Also, it seems that Journal of Algebra has been in a bit of decline in the mean time. Finally, while it it ranked the highest there, it is still not (nor was it at the time the list was made) anywhere near the level of journals like Advances (or even less Inventiones). – Tobias Kildetoft Oct 5 '17 at 12:35
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    One thing which seems not to have been mentioned: J of Alg is a specialist journal, while Math Zeit, JLMS and IMRN are all general journals. This may or may not be a factor which affects likelihood of getting your papers accepted in these other journals. – Yemon Choi Oct 5 '17 at 15:45
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    I tried rephrasing the question so it is no longer a shopping question. Apologies to the OP if I have misrepresented anything. – Kimball Oct 6 '17 at 4:23
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I don't think that "generalist vs specialist" is the right question to ask. Rather, I think that you should think of journals as being in various tiers of quality. Notice that I'll express some opinions on specific journals below, and other mathematicians might disagree with them. It is worthwhile to talk to a good number of senior people to help get a sense as to what tier various journals occupy. I don't think that impact factors are what really matters here, but rather the subjective opinions of whoever will be evaluating your cv (at least in the US, this is mostly other mathematicians).

Some subject-specific journals are really excellent (e.g. Geometry and Topology, Algebra and Number Theory, Journal of Algebraic Geometry), some are decent but not excellent (I think that the Journal of Algebra fits this bill), others are pretty terrible (I won't make a list here so as to avoid starting a debate).

It is true that the very best generalist journals (Annals, Inventiones, JAMS, Acta, Publications IHES, Duke, JEMS) occupy a higher tier than even the best subject-specific journals. However, it's not clear to me that the excellent but not top generalist journals (eg Math Zeitschrift) are clearly better than the best subject-specific journals.

You should try very hard to have your papers in the best journals that you can get to accept them. Editors at strong journals are used to getting papers that are not directly related to their research, so you shouldn't stress out about sending your papers to them.

As to your final question (about how many papers in one tier are needed to get the equivalent quality of one paper in a higher tier), the correct answer is probably "infinity". When I evaluate someone's cv, I am trying to figure out how good their best work is. One paper in the Annals trumps any number of papers in lesser journals.

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    Could you expand upon why you are trying to figure out the quality of someone's best work (as opposed to median or most common work)? Although that's not strictly speaking necessary to answer the question, I think it would be of great interest to graduate students and non-tenure faculty reading this post. I for one was quite surprised to read that. – Stella Biderman Oct 11 '17 at 22:07
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    I'll let Andy speak for himself, but this is a very common attitude among mathematics faculty especially (compared to other fields). – Tom Church Oct 11 '17 at 22:33
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    Echoing @TomChurch, and echoing Andy Putman, I, too, want to see the best that a candidate can do, not their average. I think a reason for this is that "good/average" stuff eventually becomes trite or banal, as ambient technique improves, while the really unusual stuff involves truly new ideas, and is more creative and "generative" for other peoples' work. – paul garrett Oct 11 '17 at 23:41
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    @StellaBiderman: Any well-trained mathematician can crank out an arbitrary number of routine, mediocre papers. It's much harder to do something genuinely new and profound, and these are the papers that really matter in the long run. When I'm evaluating someone (for a job, grant, etc.), my goal is to figure out who really has the potential to make that kind of serious contribution. – Andy Putman Oct 12 '17 at 1:24
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    (I should say that I'm probably one of those people who write too many papers, but I admire people who write fewer but more substantial papers) – Andy Putman Oct 12 '17 at 1:27
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As a senior PhD candidate, my opinion is as follows:

Is it considered to be much better to have a publication in such a general journal than in a specialized journal like Journal of Algebra? I made the experience that sending my papers to Journal of Algebra, one gets a much quicker publication and the editors are closer to my field. So from my side I would just send all my papers to Journal of Algebra or another specialised journal, but I assume that this will look weird in my CV. Does it harm me if I do this even when some of my papers could go into a slightly better journal like Mathematische Zeitschrift? I feel uncomfortable sending my papers to editors that are far away from my field of research.

This question has multiple aspects to be considered:

  1. Type of study: As in, where does it fall between being a theoretical paper to applied sciences. Theoretical papers are already very hard to publish and they are often too specific. In this case I do not think it is particularly bad to submit to the same journal. On the other hand, application studies can go both ways: too specific or too generic. If it is too specific, it can be better to submit to a journal which is sector specific. (i.e. You do not submit a marine application to civil engineering journal.) If it is too generic, by which I mean you do not improve a theory or propose a new method, but instead illustrate a method's performance, you should submit to a journal with a higher impact factor.
    1. Quality over Quantity: If you are required to publish a specific amount of papers annually for reasons, it should not matter in which journal you publish as long as it meets the standards. Since they are taking quantity over quality, then I do not think anyone would give a second glance to the papers. On the other hand, when quality weighs heavier, you should try to leave your comfort zone and submit to different journals too. Everybody has something to improve your work even if you get rejected. Even more considering that you may have submitted a paper to a better journal and was rejected, you can then use that information to improve your study and submit again.
    2. More on comfort zones: I think that if you are bothered by this question and you have other alternatives, then you are not comfortable being in your comfort zone. Take your chances with other journals as well. At worst you receive a rejection. If you believe in your study, why not publish it in a journal with a high impact factor and prestige. (I have been trying to get a paper accepted for a journal for 4 years. I was rejected by 12 different journals so far, with reasons varying from we are too good for you, to it's not you, it's me. I have re-written the paper twice from scratch. With each rejection I improved something and now I am more eager to publish it because it has really improved. I am now waiting for an answer from the 13th journal.)

How bad is it to have a very good paper (that might be suitable for the best general journals) published in a journal like Journal of Algebra?

If you think that you could do better than this, then yes, it is bad to publish a very good paper in a mediocre journal. Also refer to answers above.

Can one give an approximate how much worth a paper in Advances of Math (or a similar or better journal) is compared to a paper in journal of algebra? Like 3 Journal of Algebra papers = one Advances of Math paper and 6 Journal of Algebra papers = 1 Inventiones paper?

I do not know if there is an exact formula about this. I would guess impact factor is what you are looking for. The higher the impact factor, the better the recognition you will get. Also check which index a journal is under.

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    Impact factor is highly debatable. Of course, this depends on whether one interprets the "worth" of a paper as "how much will it help my career prospects", which in turn depends on "do I work in an academic system where people who affect my career prospects care about impact factor" – Yemon Choi Oct 11 '17 at 17:39
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    In the U.S., it does not appear that mathematicians care about so-called "impact factors", currently. – paul garrett Oct 11 '17 at 20:36
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    I am not a mathematician but in Turkey quantity is more important if you want tenure at state universities. Which in my opinion is very very sad. – Sahika Koyun Oct 11 '17 at 21:20
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    As in my comment above, echoing Tom Church and Andy Putman, if the metric is "maximum" of quality of journals, which is approximately the case in current mathematics in the U.S., then no number of lesser-quality journal publications is equivalent to a single highest-quality publication. In particular, from this viewpoint, "impact factor" is completely useless and misleading. E.g., 1,000 crappy papers, or 10,000, or 100,000, will not be "as good" as a single paper in The Annals of Math, for example. – paul garrett Oct 11 '17 at 23:43
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    @paulgarrett while at an abstract level I agree with your comment on "a huge number of crappy papers", I do think there is a danger on many online sites that discuss maths (MO, MSE, here, the SBS diaspora) of "let them eat brioche". Other people in other systems face other pressures and (dis)incentives. – Yemon Choi Oct 13 '17 at 16:52

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