Krull dimension of finite rings [closed]

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I have the following question(s):

Can the Krull dimension of a finite ring be any natural number?

Thanks for the help!

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1 Answer

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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.

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