Theorems · Theorem · field theory
IntermediateField.isSeparable_adjoin_pair_of_isSeparable
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {x y : E},
IsSeparable F x → IsSeparable F y → Algebra.IsSeparable F ↥F⟮x, y⟯If x and y are both separable elements, then F⟮x, y⟯ / F is a separable extension.
As a consequence, any rational function of x and y is also a separable element.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- Algebra.IsSeparablestatement and proof · cited by 210
- IsSeparablestatement and proof · cited by 68
- IsSeparable.tower_topproof · cited by 11
- IntermediateField.adjoin_simple_adjoin_simpleproof · cited by 3
- Algebra.IsSeparable.transproof · cited by 1
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