field extension in a sentence

Examples

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