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power associativity

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power associativity

As you now know, there are commutative algebras that are not power-associative. So your proof that Jordan algebras are power-associative is incorrect.

A proof that Jordan algebras are power-associative can be found in chapter IV of Richard D. Schafer's book "An Introduction to Nonassociative Algebras". (This proof is for characteristic not equal to 2. I don't know what happens when the characteristic is 2.)

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As you now know, there are commutative algebras that are not power-associative. So your proof that Jordan algebras are power-associative is incorrect. A proof that Jordan algebras are power-associative can be found in chapter IV of Richard D. Schafer's b
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