4
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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?

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  • $\begingroup$ This follows from stacks.math.columbia.edu/tag/00JB and the Cohen Structure Theorem. $\endgroup$ – Youngsu Dec 18 '17 at 0:53
  • $\begingroup$ @Youngsu where?I don't find this. $\endgroup$ – Sky Dec 18 '17 at 0:57
  • $\begingroup$ @Sky stacks.math.columbia.edu/tag/032A $\endgroup$ – Youngsu Dec 18 '17 at 1:01
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    $\begingroup$ 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 $I\subset A$. $\endgroup$ – Ravi Dec 18 '17 at 3:19

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