There seems to be a symmetry between properties of vector spaces and field extensions.
Let us create some small dictionary:
vector space over a field - field extension of a field
linear independence - algebraic independence
linear matroid - algebraic matroid
dimension - transcendence degree
What I want to know is: does there exist a common abstraction for both vector spaces and field extensions in which one can treat both of these in a unified way and derive the mentioned items of the dictionary (and hopefully much more) as special cases of the general framework?