 A vector field can be visualized as assigning a vector to individual points within an "n"-dimensional space.Given two "Ck"-vector fields "V", "W" defined on "S" and a real valued "Ck"-function "f" defined on "S", the two operations scalar multiplication and vector addition

define the module of "Ck"-vector fields over the ring of C"k"-functions where the multiplication of the functions is defined pointwise (therefore, it is commutative with the multiplicative identity being "fid(p)