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