One of my article is pure mathematics is going to appear in a journal soon. The journal shared with me the reprint version to check if I have any correction and I confirmed it. Also transferred copyright issue. They sent me the final (published) version. The journal website has published the issue.
Can I upload my reprint in research-gate or arxiv database now?
When you transferred copyright you should have gotten a contract that lists what you are allowed to do. In the absence of that, ask the editor you communicated with.
As you note, in math it is common to permit the author to upload some version of the paper, but perhaps not the final published version. And since you don't have copyright anymore you have to abide by the journal's rules. Ask, don't assume.
Check the publisher's policies. Here's the page for Elsevier. To quote:
The Published Journal Article cannot be shared publicly, for example, on ResearchGate or Academia.edu, to ensure the sustainability of peer-reviewed research in journal publications.
So you cannot post it on ResearchGate. If you published with another publisher they might have different policies.
Check the journal/publisher policies, but you will almost certainly find that these draw a distinction between the published version and the author accepted manuscript. The author accepted manuscript is the final version you gave them. The published version is the one they subsequently gave you, which will have some changes of questionable value including their own formatting.
What people normally do in pure math is to put the author accepted manuscript on arXiv. This is almost always permitted (all the big commercial publishers allow it). ArXiv probably won't even accept the published version, not for copyright reasons but because they require the source files which you won't normally have access to.
Unless you are publishing open access, you usually can't upload the published version anywhere publicly accessible. You also normally can't put the author accepted manuscript on ResearchGate, since the permission to put it on arXiv is usually specific to a small number of sites. E.g Elsevier's policy says
Authors can share their accepted manuscript [...] By updating a preprint in arXiv or RePEc with the accepted manuscript (and updating the license to a CC BY-NC-ND license) [...]
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