  Let $B$ be a finitely generated algebra over a field $k$. Then $B$ is called
a Jacobson algebra if every semiprime ideal of $B$ is semiprimitive. We will
discuss several conditions, all involving the commutant of simple $B$-modules,
which imply that $B$ is Jacobson. In particular, we will recover the well-known
result that every finitely generated almost commutative algebra is Jacobson.
The same holds true for $\mathbb{N}$-filtered $k$-algebras $B$ with a locally
finite filtration such that the associated graded $k$-algebra is
left-noetherian.
