Theorems · Theorem · field theory
IntermediateField.exists_lt_finrank_of_infinite_dimensional
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] [Algebra.IsAlgebraic F E],
¬FiniteDimensional F E → ∀ (n : ℕ), ∃ L, FiniteDimensional F ↥L ∧ n < Module.finrank F ↥LIf E / F is an infinite algebraic extension, then there exists an intermediate field
L / F with arbitrarily large finite extension degree.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Bot.botproof · cited by 4,720
- LE.le.transproof · cited by 3,151
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinproof · cited by 382
- Algebra.IsAlgebraicstatement and proof · cited by 322
- not_ltproof · cited by 306
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
Cited by3
Results whose statement or proof uses this declaration.
- Field.finSepDegree_eq_finrank_of_isSeparableproof · cited by 7
- IntermediateField.finrank_eq_fixingSubgroup_indexproof · cited by 1
- IsGalois.finiteDimensional_of_finiteproof · cited by 1