Tensor product of division rings is Noetherian

Question

Let $k$ be a field and $D_{1},D_{2}$ division rings which are finite dimensional over $k$. Is it true that $D_{1} \otimes_{k} D_{2}$ is Noetherian?

Can we say that yes since the tensor product is just some number of copies of the field $k$?

Answer 1

Since the tensor product is a finite dimensional algebra, it is noetherian.