TITLE: What if your research paper got rejected with few comments given on  paper?
QUESTION [12 upvotes]: I often wonder what if your research paper got rejected?  Is it fair enough to resubmit that paper in the same journal? Is there any possibility of publication of that paper in any journal?
Thanks

REPLY [2 votes]: Sometimes a paper might be rejected just because it doesn't meet the journal's high standards, not because there's anything really wrong with it. However, if a referee makes any substantive criticisms, it's almost always a mistake to submit the paper to another journal without making some revisions.

From "Advice for amateur mathematicians on writing and publishing papers"
http://math.mit.edu/~cohn/Thoughts/advice.html
(Henry Cohn's website)
And some other things to remember:

If your paper is rejected, you can submit it to another journal, but you should not resubmit a revised version to the same journal unless they explicitly invite you to do so (which rarely happens).
Choose a journal that publishes papers like yours (in terms of topic, style, length, importance, etc.). If you're not sure, go to the library and flip through some back issues until you find one that looks suitable. A good starting point is the journals that published the papers you cite. Each issue of a journal should explain where to send submissions.
You cannot submit the same paper to two journals at once. If you are caught doing this, the editors will be angry with you and it will be hard to get your paper published. (You should also not submit simultaneously to two different editors at the same journal.)