A contravariant functor $F$ from monoids to commutative rings was defined there.
Question. What is the Krull dimension of $F(\mathbb N)$?
(Here $\mathbb N$ denotes the additive monoid $(\mathbb N,+)$.)
(If $G$ is a finite group, then $F(G)$ is the Burnside ring of $G$.)
This question is inspired by this outstanding answer of Eric Wofsey.