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There are at least three mutually non-isomorphic rings with $4$ elements?

How can I prove how many rings are commutative, unitary with 4 elements?

(obviously isomorphism doesn't matter) I don't know it is something about quaternions. It seems trivial but I don't know.

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  • I think that this question is essentially a duplicate of another recent question. May be not an exact duplicate, but the answers in the linked question cover it all IMHO. – Jyrki Lahtonen Jan 29 '13 at 10:11
  • Yes, it's a duplicate. Thus, voting to close as such. – Johannes Kloos Jan 29 '13 at 10:15
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    +1 to Martin's answer. The exact same list was constructed in the discussion of the linked question, which is why I think this is essentially duplicate. Others may take a different view, and that discussion is better moved to meta. Actually the meta-thread on abstract duplicates probably covers this. – Jyrki Lahtonen Jan 29 '13 at 12:00

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