A vector space over is a set of Vectors for which any Vectors , , and and any Scalars , have the following properties:
A Module is abstractly similar to a vector space, but it uses a Ring to define Coefficients instead of the Field used for vector spaces. Modules have Coefficients in much more general algebraic objects.
See also Banach Space, Field, Function Space, Hilbert Space, Inner Product Space, Module, Ring, Topological Vector Space
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press,
pp. 530-534, 1985.