field extension in a sentence

Examples

1. The difficulty is this : class field theory is about certain things called abelian field extensions.
2. The dimension of " U " will be equal to the transcendence degree of this field extension.
3. *PM : simple transcendental field extension, id = 6751-- WP guess : simple transcendental field extension-- Status:
4. A field extension E \ supseteq F is "'separable "', if is the separable closure of in.
5. Also notable is the Hilbert class field, the maximal abelian unramified field extension of " F ".
6. *PM : simple transcendental field extension, id = 6751-- WP guess : simple transcendental field extension-- Status:
7. Uniruledness is a geometric property ( it is unchanged under field extensions ), whereas ruledness is not.
8. Usually one is looking for solutions in the so-called universal family of difference field extensions of K.
9. Extended Euclidean algorithm is also the main tool for computing multiplicative inverses in simple algebraic field extensions.
10. Finite-rank matroids include any subsets of finite-dimensional vector spaces and of field extensions of finite transcendence degree.