Theorems · Definition · field theory
Subfield.relfinrank
{E : Type v} → [inst : Field E] → Subfield E → Subfield E → ℕThe Nat version of Subfield.relrank.
If B / A ⊓ B is an infinite extension, then it is zero.
- Defined in
- Mathlib.FieldTheory.Relrank
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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.
- Fieldstatement and proof · cited by 7,404
- Module.finrankproof · cited by 1,770
- Subfieldstatement and proof · cited by 303
- Subfield.extendScalarsproof · cited by 17
Cited by24
Results whose statement or proof uses this declaration.
- IntermediateField.relfinrankproof · cited by 27
- Subfield.relfinrank_eq_one_iffstatement · cited by 2
- Subfield.relfinrank_eq_one_of_lestatement · cited by 1
- Subfield.relfinrank_eq_toNat_relrankstatement · cited by 1
- Subfield.relfinrank_inf_mul_relfinrank_of_lestatement · cited by 1
- Subfield.relfinrank_mul_finrank_topstatement · cited by 1
- Subfield.relfinrank_selfstatement · cited by 1
- Subfield.relfinrank_comapstatement · cited by 0
- Subfield.relfinrank_comap_comap_eq_relfinrank_infstatement · cited by 0
- Subfield.relfinrank_comap_comap_eq_relfinrank_of_lestatement · cited by 0
- Subfield.relfinrank_comap_comap_eq_relfinrank_of_surjectivestatement · cited by 0
- Subfield.relfinrank_dvd_finrank_top_of_lestatement · cited by 0