Let $A$ be a noetherian ring, $\mathfrak{m}$ a maximal ideal, and $\mathfrak{q}$ is $\mathfrak{m}$-primary. Then $A/\mathfrak{q}$ is a 1;;local artinian ring.

Proof:

1. quotient of noetherian rings are noetherian
2. Use previous corollary
3. Apply 13. Proposition 4.8.6