Theorems · Theorem · field theory
Field.finSepDegree_eq_zero_of_transcendental
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [Algebra.Transcendental F E], Field.finSepDegree F E = 0
If the field extension E / F is transcendental, then Field.finSepDegree F E = 0, which
actually means that Field.Emb F E is infinite (see Field.infinite_emb_of_transcendental).
- 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.
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
- Nat.card_eq_zero_of_infiniteproof · cited by 46
- Field.finSepDegreestatement · cited by 24
- Algebra.Transcendentalstatement and proof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- isPurelyInseparable_of_finSepDegree_eq_oneproof · cited by 1