I have the following question(s):
Can the Krull dimension of a finite ring be any natural number?
Thanks for the help!
2026-03-28 22:28:10.1774736890
Krull dimension of finite rings
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Any finite ring is Artinian, and hence has Krull dimension zero. The reason is, that in any Artinian ring every prime ideal is maximal.
References: Theorem 8.5 of Atiyah MacDonald.