Aren't these the standard vector space axioms? I seem to recall that they were defined in a quite similar way in my class. Of course, you can simply the defini

Aren't these the standard vector space axioms? I seem to recall that they were defined in a quite similar way in my class. Of course, you can simply the definition if you can say "vector spaces form a group and also satisfy these axioms with respect to scalar multiplication", but then you need to introduce groups first, which would be a distraction.