| 31. | The curves obtained are isomorphic to the starting curve over the field extension given by the twist degree.
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| 32. | All finite transcendence degree field extensions of " k " correspond to the rational function field of some variety.
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| 33. | Connections underpinned by Galois theory show that certain finite degree field extensions may be analysed via finite group theory.
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| 34. | In more advanced mathematics they play an important role in ring theory, especially in the construction of field extensions.
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| 35. | :If you have a field extension L over a base field K, then L has a K vector space structure.
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| 36. | This implies that the degree of the field extension generated by a constructible point must be a power of 2.
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| 37. | An separable if the base extension A \ otimes _ k F is semisimple for any field extension F / k.
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| 38. | In which case, you can't really say anything about the degree of the relevant field extensions before you know they're irreducible?
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| 39. | This class has the amalgamation property since any two field extensions of a prime field can be embedded into a common field.
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| 40. | :It is the field extension obtained by adjoining all polynomials in the algebraic number & xi; to the field of rational numbers.
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