Theorems · Definition · field theory
Field.finInsepDegree
(F : Type u) → (E : Type v) → [inst : Field F] → [inst_1 : Field E] → [Algebra F E] → ℕ
The finite inseparable degree for a general field extension E / F is defined
to be the degree of E / separableClosure F E as a natural number. It is defined to be zero
if such field extension is infinite.
- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 15 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.
Cites4
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
- Module.finrankproof · cited by 1,770
- separableClosureproof · cited by 55
Cited by15
Results whose statement or proof uses this declaration.
- Field.finInsepDegree_def'statement · cited by 2
- Field.finInsepDegree_eq_of_equivstatement · cited by 1
- Field.finInsepDegree_selfstatement · cited by 1
- Field.finInsepDegree_top_le_finInsepDegree_of_isScalarTowerstatement · cited by 1
- IntermediateField.finInsepDegree_le_of_left_lestatement · cited by 0
- Algebra.IsSeparable.finInsepDegree_eqstatement · cited by 0
- finInsepDegree_eq_powstatement · cited by 0
- Field.finInsepDegree_mul_finInsepDegree_of_isAlgebraicstatement · cited by 0
- IntermediateField.finInsepDegree_botstatement · cited by 0
- IntermediateField.finInsepDegree_bot'statement · cited by 0
- IntermediateField.finInsepDegree_topstatement and proof · cited by 0