Does a countable integral domain have only finitely many maximal ideals?
I've been thinking about this for awhile, I'd really appreciate a proof or counter example!! Thanks!
2026-03-29 11:43:35.1774784615
Does a countable integral domain have only finitely many maximal ideals?
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Not necessarily. A counterexample is $\mathbf Z$: its maximal ideals are generated by the primes and, as as you know, there's an infinity of them.