Theorems · Theorem · complex analysis
Real.nonempty_algEquiv_or
∀ (F : Type u_1) [inst : Field F] [inst_1 : Algebra ℝ F] [Algebra.IsAlgebraic ℝ F], Nonempty (F ≃ₐ[ℝ] ℝ) ∨ Nonempty (F ≃ₐ[ℝ] ℂ)
An algebraic extension of ℝ is isomorphic to either ℝ or ℂ as an ℝ-algebra.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 296 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Complexstatement · cited by 5,565
- AlgEquivstatement · cited by 1,681
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Complex.finrank_real_complexproof · cited by 11
- IsAlgClosed.nonempty_algEquiv_or_of_finrank_eq_twoproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- NormedAlgebra.Real.nonempty_algEquiv_orproof · cited by 0