Definition 3

Let $V_1, V_2$ be two right vector spaces over $\mathbf{K}$ with $\mathbf{K}'$-structures $V'_1, V'_2$ respectively. A $\mathbf{K}$-linear mapping $f : V_1 \to V_2$ is said to be rational over $\mathbf{K}'$ if $f(V'_1) \subset V'_2$.

If $V_3$ is a third right vector space over $\mathbf{K}$, with a $\mathbf{K}'$-structure $V'_3$ and a $\mathbf{K}$-linear mapping $g : V_2 \to V_3$ is rational over $\mathbf{K}'$, clearly $g \circ f : V_1 \to V_3$ is rational over $\mathbf{K}'$.