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I have written an almost 30-page paper in mathematics (in number theory). The paper contains two parts.

The first part is an independent study, which is a generalisation of previous work by other mathematicians, while the second part of the paper depends on the first part. To be precise, I have used one result from the first part in the second part. Each part is written in different sections.

The second part is a generalisation of a previous publication in a Q3 quartile and an international peer-reviewed journal, published by Pleiades Publishing and distributed by Springer. To give some idea, by generalisation, I mean I have generalised the previous results in a higher-dimensional case.

The reason I am giving details about the journal is because, recently, I got a rejection of the current paper, which consists of two parts mentioned above. The referee report says:

Since the first part of the paper is a strict generalisation of the previous work and since the second part is a generalisation of the previous published paper (which was published in an ordinary journal) of the authors, I don't recommend publication in this journal. The author can submit it to another journal. The referee gave some minor suggestion.

I am not sure if it is reasonable to judge the work of a paper by looking at its parent paper's journal. Interestingly, both journals (the journal where the previous paper was published and the journal that rejected the current paper) are in Q3 quartile.

Anyway, I have a plan to divide the paper into two separate parts. This is because, for the first part, I have found one nice application that will make it more appealing. I want to divide because I am worried that the second part might dilute the overall optics of the combined-paper, especially after the referee report. If I divide, then I don't have to cite the published paper (which I cited in the second part of the paper) for the first part (to be a single paper).

The second part (to be another single paper) can be sent to an ordinary journal, as hinted by the referee, while the first paper (due to its new-found) application) can find a good journal.

But the problem is that, the whole paper is in arXiv database, so for the second paper, I have to cite the arXiv paper. That seems awkward.

Should I divide the paper? Should I also upload separate parts to Arxiv while the combined-paper is already in Arxiv?

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    Regarding the Arxiv version, that is precisely one of the things the comment field is for. I.e. once both are published you can simply update this to say something like "Sections 1-N appeared as ... and sections N+1 - M as ...".
    – mlk
    Commented Aug 17 at 13:19
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    SCNR: Of course you can divide the paper, just not by zero.
    – Peter - Reinstate Monica
    Commented Aug 18 at 3:58

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The general (headline) question's answer is "it depends". It depends on the paper and on the journal. However, it is a good idea to follow the advice of reviewers and editors.

So, in this case, it might be best to separate the paper into two and make independent submission decisions. After separation, you might be able to expand on the second part and have something more substantial.

Don't worry about the ArXiv issue. It is what it is. Papers there are not usually assumed to be in their final form. Cite, of course.

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