21. The difficulty is this : class field theory is about certain things called abelian field extensions . 22. The dimension of " U " will be equal to the transcendence degree of this field extension . 23. *PM : simple transcendental field extension, id = 6751-- WP guess : simple transcendental field extension -- Status: 24. A field extension E \ supseteq F is "'separable "', if is the separable closure of in. 25. Also notable is the Hilbert class field, the maximal abelian unramified field extension of " F ". 26. *PM : simple transcendental field extension , id = 6751-- WP guess : simple transcendental field extension-- Status: 27. Uniruledness is a geometric property ( it is unchanged under field extensions ), whereas ruledness is not. 28. Usually one is looking for solutions in the so-called universal family of difference field extensions of K. 29. Extended Euclidean algorithm is also the main tool for computing multiplicative inverses in simple algebraic field extensions . 30. Finite-rank matroids include any subsets of finite-dimensional vector spaces and of field extensions of finite transcendence degree.
