Let $A$ be a finite-dimensional $k$-algebra, with $k$ a field. I know (and have also seen it at this site) that $\mathrm{Spec}(A)$ is $k$-isomorphic to a Proj-scheme $\mathrm{Proj}(B) \mapsto \mathrm{Spec}(k)$ for some graded commutative ring $B$. How does $B$ look like ?
What about if $A$ is a finitely generated $C$-algebra, with $C$ a commutative ring ?