Theorems · Theorem · field theory
Field.finSepDegree_dvd_finrank
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E], Field.finSepDegree F E ∣ Module.finrank F E
The separable degree of any field extension E / F divides the degree of E / F.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Top.topproof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Bot.botproof · cited by 4,720
- FiniteDimensionalproof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- IntermediateFieldproof · cited by 988
- IntermediateField.adjoinproof · cited by 382
- IntermediateField.restrictScalarsproof · cited by 66
- dvd_zeroproof · cited by 63
- finrank_topproof · cited by 31
- Module.finrank_mul_finrankproof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- Field.finSepDegree_le_finrankproof · cited by 1