  Let $S^{\cdot}$ be a noetherian graded algebra over a commutative $k$-algebra
$A$, where $k$ is a commutative ring, and assume it is a module over a Lie
algebroid ${\mathfrak g}_{A/k}$. If $S^\cdot$ is semi-simple over ${\mathfrak
g}_{A/k}$ we prove that its ring of invariants $\bar S^{\cdot}$ is notherian.
When ${\mathfrak g}_{A/k}$ is a solvable Lie algebra over $A$ we construct
noetherian subalgebras of $S^\cdot$ from subsets of characters of ${\mathfrak
g}_{A/k}$. We give similar results for noetherian modules over the pair
$(S^{\cdot}, {\mathfrak g}_{A/k})$.
