Theorems · Definition · field theory
IntermediateField.relfinrank
{F : Type u} →
{E : Type v} →
[inst : Field F] → [inst_1 : Field E] → [inst_2 : Algebra F E] → IntermediateField F E → IntermediateField F E → ℕThe Nat version of IntermediateField.relrank.
If B / A ⊓ B is an infinite extension, then it is zero.
- Defined in
- Mathlib.FieldTheory.Relrank
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 91 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
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.toSubfieldproof · cited by 38
- Subfield.relfinrankproof · cited by 23
Cited by27
Results whose statement or proof uses this declaration.
- IntermediateField.relfinrank_eq_one_iffstatement · cited by 2
- IntermediateField.relfinrank_eq_one_of_lestatement · cited by 2
- IntermediateField.relfinrank_mul_finrank_topstatement · cited by 2
- IntermediateField.finrank_bot_mul_relfinrankstatement · cited by 1
- IntermediateField.relfinrank_inf_mul_relfinrank_of_lestatement · cited by 1
- IntermediateField.inf_relfinrank_rightstatement · cited by 1
- IntermediateField.finrank_comapstatement · cited by 0
- IntermediateField.relfinrank_bot_leftstatement · cited by 0
- IntermediateField.relfinrank_bot_rightstatement · cited by 0
- IntermediateField.relfinrank_comapstatement · cited by 0
- IntermediateField.relfinrank_comap_comap_eq_relfinrank_infstatement · cited by 0
- IntermediateField.relfinrank_comap_comap_eq_relfinrank_of_lestatement · cited by 0