Theorems · Theorem · field theory
IntermediateField.adjoin_simple_toSubalgebra_of_isAlgebraic
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {α : E},
IsAlgebraic F α → F⟮α⟯.toSubalgebra = F[α]- Cited by
- 7 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- IntermediateField.adjoinstatement · cited by 382
- IsAlgebraicstatement and proof · cited by 163
- IntermediateField.toSubalgebrastatement · cited by 134
- IntermediateField.adjoin_toSubalgebra_of_isAlgebraicproof · cited by 10
Cited by7
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtensionproof · cited by 4
- IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_twoproof · cited by 4
- IsGalois.is_separable_splitting_fieldproof · cited by 2
- isSplittingField_X_pow_sub_C_of_root_adjoin_eq_topproof · cited by 1
- IsLocalRing.exists_adjoin_eq_topproof · cited by 0
- IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoinproof · cited by 0
- NumberField.adjoin_eq_top_of_infinitePlace_ltproof · cited by 0