After a confusing session of hopping through Wikipedia articles, I started trying to summarize for myself some of the inclusions and relations among the many types of integral domains. Right now I'm just gathering and organizing facts from various sources, rather than going through all the proofs in detail. (To be honest, my knowledge of commutative algebra is embarrassingly poor, and I haven't even understood all of the definitions yet. But one has to start somewhere...)
Anyway, I have a few questions about things that I haven't been able to figure out on my own, and I'll start with this one:
Are there Krull domains that are neither Noetherian nor UFD?
(I would guess yes, but I haven't seen any examples. The standard example of a non-Noetherian Krull domain seems to be $\mathbf{Z}[X_1,X_2,\dots]$ with countably many variables, but that's a UFD unless I'm mistaken. And $\mathbf{Z}[\sqrt{-5}]$ is a non-UFD which is a Dedekind domain, hence a Krull domain and Noetherian.)