Is there a non-artinian noetherian ring whose non-units are zero-divisors?
Is there a noetherian ring of positive dimension whose non-units are zero-divisors?
[In this post, "ring" means "commutative ring with one", and "dimension" means "Krull dimension".]
Here is the motivation:
Let $A$ be a ring whose non-units are zero-divisors.
If $A$ is not noetherian, then $A$ can have positive dimension: see this answer of user18119.
If $A$ is noetherian and reduced, then $\dim A\le0$: see this answer of user26857.
[Recall that a noetherian ring is artinian if and only if its dimension is $\le0$. Recall also that a ring has the property that its non-units are zero-divisors if and only if it is isomorphic to its total ring of fractions.]