Theorems · Definition · field theory
Field.sepDegree
(F : Type u) → (E : Type v) → [inst : Field F] → [inst_1 : Field E] → [Algebra F E] → Cardinal.{v}The (infinite) separable degree for a general field extension E / F is defined
to be the degree of separableClosure F E / F.
- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Fieldstatement and proof · cited by 7,404
- Cardinalstatement · cited by 2,598
- Module.rankproof · cited by 496
- separableClosureproof · cited by 55
Cited by24
Results whose statement or proof uses this declaration.
- Field.sepDegree_eq_of_equivstatement · cited by 2
- IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparablestatement and proof · cited by 2
- Field.lift_rank_mul_lift_sepDegree_of_isSeparablestatement and proof · cited by 2
- Field.lift_sepDegree_eq_of_equivstatement · cited by 2
- Field.lift_sepDegree_mul_lift_sepDegree_of_isAlgebraicstatement and proof · cited by 2
- Field.finSepDegree_eqstatement · cited by 2
- Field.sepDegree_eq_of_isPurelyInseparablestatement and proof · cited by 1
- Field.sepDegree_eq_of_isPurelyInseparable_of_isSeparablestatement · cited by 1
- Field.sepDegree_mul_insepDegreestatement · cited by 1
- Field.sepDegree_mul_sepDegree_of_isAlgebraicstatement and proof · cited by 1
- Field.sepDegree_selfstatement · cited by 1
- IsPurelyInseparable.sepDegree_eq_onestatement · cited by 1