| Popis: |
This final chapter deals with another important result on primitive elements: given an extension E/F of Galois fields with degree n ≥ 2, usually every affine F-hyperplane of E contains a primitive element. The proof will take up almost all of this chapter; some motivation and a detailed outline is provided in the introductory first section. In the final two sections, we consider an interesting application of finite fields for which the strongest known results rely on theorems concerning primitive elements that are quite similar in spirit to those considered in the main part of this chapter and in Chap. 13, and we also include a brief discussion of some existence results for primitive elements satisfying various additional requirements. |
