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