Is there a finite dimensional local ring with infinitely many minimal prime ideals?
Equivalent formulation:
Is there a ring with a prime ideal $\mathfrak p$ of finite height such that the set of minimal prime sub-ideals of $\mathfrak p$ is infinite?
Here "ring" means "commutative ring with one", "dimension" means "Krull dimension", and "local ring" means "ring with exactly one maximal ideal" (warning: some authors call "quasi-local ring" a ring with exactly one maximal ideal, and "local ring" a noetherian ring with exactly one maximal ideal; it is well known that a noetherian ring has only finitely many minimal prime ideals).
from Hot Weekly Questions - Mathematics Stack Exchange
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