Ein Beweis für die Existenz von Normalbasen in endlichen Körpern. (A proof for the existence of normal bases in finite fields) (Q580432)

Let K be a finite field and L a finite extension field of K. Then it is well-known that there exists an element \(x\in L\) such that the conjugates of x form a basis for the linear space L over K. If G denotes the Galois group of L/K then the above theorem is equivalent with the statement, that L is a cyclic GK-module. The paper gives a new proof for this theorem using lattice properties of the GK-submodules of L.