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Possible Duplicate:
Property of commutative rings

Show a simple proof that if $R$ is a ring such that $x^{3}=x$ for all $x\in R$ then $R$ is commutative. (You don't need the Jacobson radical, I'll provide proof if this remains unanswered too long.)

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Steven Gamer
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    Duplicate of http://math.stackexchange.com/questions/67148/property-of-commutative-rings, see also http://math.stackexchange.com/questions/16535/is-such-ring-commutative http://math.stackexchange.com/questions/76792/ring-such-that-x4-x-for-all-x – Matthew Towers Jan 31 '13 at 16:10
  • Only one of the links above is a duplicate. The others consider related problems such as $, x^n = x:$ for $:n = 4,5,:$ whose proofs do not apply to this case. – Math Gems Jan 31 '13 at 19:26

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