Theorems · Theorem · field theory
IsAlgClosed.nonempty_algEquiv_or_of_finrank_eq_two
∀ {F : Type u_1} {F' : Type u_2} (E : Type u_3) [inst : Field F] [inst_1 : Field F'] [inst_2 : Field E]
[inst_3 : Algebra F F'] [inst_4 : Algebra F E] [Algebra.IsAlgebraic F E] [IsAlgClosed F'],
Module.finrank F F' = 2 → Nonempty (E ≃ₐ[F] F) ∨ Nonempty (E ≃ₐ[F] F')- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- AlgHomproof · cited by 3,236
- Module.finrankstatement and proof · cited by 1,770
- AlgEquivstatement and proof · cited by 1,681
- Subalgebraproof · cited by 1,353
- Algebra.IsAlgebraicstatement and proof · cited by 322
- AlgHom.rangeproof · cited by 169
- IsAlgClosedstatement and proof · cited by 150
- AlgEquiv.transproof · cited by 108
Cited by1
Results whose statement or proof uses this declaration.
- Real.nonempty_algEquiv_orproof · cited by 1