11. ;"'Transcendence degree "': The number of algebraically independent transcendental elements in a field extension . 12. Let E / F be a finite degree field extension . 13. A subextension of a finitely generated field extension is also a finitely generated extension. 14. Let L / K be a finite field extension . 15. A difference algebra which is a field is called a " difference field extension ". 16. Alternatively, constructing such field extensions can also be done, if a bigger container is already given. 17. But this is a cyclic field extension , and so must contain a primitive root of unity. 18. Let K be a global field and let L / K be a finite field extension . 19. A field extension is called a cyclic extension if its Galois group is a cyclic group. 20. By using analytic continuation to eliminate field, in fact a field extension of the complex numbers.
