field extension in a sentence

Examples

1. ;"'Transcendence degree "': The number of algebraically independent transcendental elements in a field extension.
2. Let E / F be a finite degree field extension.
3. A subextension of a finitely generated field extension is also a finitely generated extension.
4. Let L / K be a finite field extension.
5. A difference algebra which is a field is called a " difference field extension ".
6. Alternatively, constructing such field extensions can also be done, if a bigger container is already given.
7. But this is a cyclic field extension, and so must contain a primitive root of unity.
8. Let K be a global field and let L / K be a finite field extension.
9. A field extension is called a cyclic extension if its Galois group is a cyclic group.
10. By using analytic continuation to eliminate field, in fact a field extension of the complex numbers.