sentences:  Since vector spaces over "K" (as a field) are the same thing as modules over the ring "K", "K"-Vect is a special case of "R"-Mod, the category of left "R"-modules.Much of linear algebra concerns the description of "K"-Vect.For example, the dimension theorem for vector spaces says that the isomorphism classes in "K"-Vect correspond exactly to the cardinal numbers, and that "K"-Vect is equivalent to the subcategory of "K"-Vect which has as its objects the vector spaces "K""n", where "n" is any cardinal number.