Normal basis theorem - Revision history

Vipul: Created page with "==Statement== Suppose $L/K$ is a finite Galois extension of fields with Galois group $G$ . Then, there exists an element $\alpha \in L$
2012-01-07T20:34:12Z

Created page with "==Statement== Suppose <math>L/K</math> is a finite Galois extension of fields with Galois group <math>G</math>. Then, there exists an element <math>\alpha \in L</mat..."

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==Statement==

Suppose <math>L/K</math> is a [[finite Galois extension]] of [[field]]s with [[Galois group]] <math>G</math>. Then, there exists an element <math>\alpha \in L</math> such that the set:

<math>\! \{ \sigma(\alpha) \mid \sigma \in G \}</math>

forms a basis for <math>L</math> as a vector space over <math>K</math>. In other words, we can always find a basis that is a single orbit under the action of the Galois group. Such a basis is termed a ''normal basis''.