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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!

user26857
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LSt
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  • Possible duplicate of http://math.stackexchange.com/questions/270982/proof-that-prime-ideals-of-finite-ring-are-maximal – user26857 Feb 22 '16 at 15:47
  • The suggested duplicate certainly answers the question, although the questions are entirely different... – rschwieb Feb 22 '16 at 18:24

1 Answers1

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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.

Dietrich Burde
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