Modules over Fields

Let $k$ be a field. As it turns out a module over a field satisfies all the properties of a vector space. Thus, ==$k$-modules are equivalent to $k$-vector spaces==. Consider the $k$-module $k^n$ where $k^n=\{(k_1,\dots ,k_n)|k_i\in k\}.$ Then, $k$ acts on $k^n$ by scalar multiplication.