Often in mathematical writing I read (and write) constructions such as
For G a finite group, the character algebra is defined as ...
For X and Y sets, a function from X to Y is ...
The general structure here is
For NAME a TYPE, SOMETHING is true
i.e. we give something of a certain type a name, and then state some property or definition.
I'm not a native speaker, so I'm wondering if these constructions are correct in standard English, or if it is simply a product of a lot of non-native speakers contributing to science, and adding their own language's quirks into their writing.
My questions: Does it have a name? Is it formally/grammatically correct?