Vector Space over Division Subring/Examples/Real Numbers in Complex Numbers

Example of Vector Space over Division Subring
Consider the field of complex numbers $\struct {\C, +, \times}$, which is a ring with unity whose unity is $1$.

Consider the field of real numbers $\struct {\R, +, \times}$, which is a division subring of $\struct {\C, +, \circ}$ such that $1 \in \R$.

Then $\struct {\C, +, \times_\R}_\R$ is an $\R$-vector space, where $\times_\R$ is the restriction of $\times$ to $\R \times \C$.