Currently, I use the Extra field in order to add the MathSciNet and Zbl identifiers. For example:
MathSciNet: MR857677 (87j:14048)
zbMATH: 57546
Zbl: 0771.14012

For
https://mathscinet.ams.org/mathscinet/relay-station?mr=MR857677
and
https://zbmath.org/?q=an:0771.14012

I'd like having them as specific item fields, not in Extra. I know they are specific of maths field, but PMID, PMCID are also specific from health fields, not generic for any field area, and they have specific Zotero item fields.

Note also that in the zbmath citation export (as .bib), both fields zbMATH and Zbl are included.
Note that MR string is included in AMS referencing style: https://subjectguides.york.ac.uk/referencing-style-guides/ams-lms
And Zbl strings must be included at least for Zentralblatt Math reviews https://www.zentralblatt-math.org/static/citation-a4.pdf (but also in Annals of Mathematics reference style, see next post).
Regarding the zbMATH number, see https://tex.stackexchange.com/a/711609/8639


Thank you!