Can the Krull dimension of the ring of holomorphic functions on an almost complex manifold be non-zero and finite?

Can the $\mathbb{C}$-algebra of holomorphic functions on an almost complex manifold be isomorphic to $\mathbb{C}[[z]]$?

The almost complex structure cannot be integrable. The simplest smooth manifold to consider is probably the unit ball of real dimension 4.

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