A definition first:
A complex algebra is a vector space $X$ over the complex field $\mathcal{C}$ in which a multiplication is defined that satisfies:
$$ x(yz) = (xy)z \\ (x + y)z = xz + yz \\ x(y + z) = xy + xz $$
and
$$ \alpha(xy) = (\alpha x) y = x (\alpha y) $$
Unless I am missing something a complex algebra seems a stricter case of ring, my question is if there're any examples of vector spaces constructed over complex algebra or at least modules over complex algebras.
I cannot find much around, but I guess there must be examples.
Clarification: The question is if $A$ is a complex algebra over a vector space $X$ I wonder if we can construct a module/vector space $Y$ where the scalar field on $Y$ are elements of $X$.