Theorems · Theorem · field theory
separableClosure.adjoin_le
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K : Type w) [inst_3 : Field K] [inst_4 : Algebra F K] [inst_5 : Algebra E K] [IsScalarTower F E K], IntermediateField.adjoin E ↑(separableClosure F K) ≤ separableClosure E K
If K / E / F is a field extension tower, then E adjoin separableClosure F K is contained
in separableClosure E K.
- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- SetLike.coestatement · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerstatement and proof · cited by 3,896
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- separableClosurestatement · cited by 55
- IntermediateField.adjoin_le_iffproof · cited by 28
- separableClosure.le_restrictScalarsproof · cited by 4
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