Talk:Normal extension

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[edit] Highly ambiguous wording

The article reads:

"The following conditions are equivalent to L / K being a normal extension:

• Let be an algebraic closure of K containing L. Every embedding σ of L in Ka which restricts to the identity on K, satisfies σ(L) = L. In other words, σ is an automorphism of L over K.
• Every irreducible polynomial in K[X] which has a root in L factors into linear factors in L[X]."

This might be saying that the conjunction of these two conditions is what's equivalent to L / K being a normal extension. Then again it might be saying that each of the two conditions is equivalent to L / K being a normal extension.

It's important to avoid such ambiguity.Daqu 21:49, 3 December 2007 (UTC)