# Commutative local, artinian ring a homomorphic image of Noetherian (local) domain?

All rings are commutative with unity.

Is every local, Artinian ring a homomorphic image of a Noetherian local domain?

If this is not true, then, at least,
Is every local, Artinian ring a homomorphic image of a Noetherian domain?

• This follows from stacks.math.columbia.edu/tag/00JB and the Cohen Structure Theorem. – Youngsu Dec 18 '17 at 0:53
• @Youngsu where？I don't find this. – Sky Dec 18 '17 at 0:57
• – Youngsu Dec 18 '17 at 1:01
• Maybe the comment you want in conjunction with the Cohen structure theorem is that every Artinian ring is $I$-adically complete with respect to any ideal $I\subset A$. – Ravi Dec 18 '17 at 3:19