Theorems · Theorem · field theory
IntermediateField.adjoin_toSubalgebra_of_isAlgebraic
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] {S : Set E},
(∀ x ∈ S, IsAlgebraic F x) → (IntermediateField.adjoin F S).toSubalgebra = Algebra.adjoin F S- Cited by
- 10 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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_eq_algebra_adjoinproof · cited by 2
- Algebra.IsIntegral.inv_memproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin_simple_toSubalgebra_of_isAlgebraicproof · cited by 7
- IntermediateField.sup_toSubalgebra_of_isAlgebraic_rightproof · cited by 6
- IntermediateField.adjoin_eq_top_iff_of_isAlgebraicproof · cited by 3
- IsCyclotomicExtension.isSeparableproof · cited by 3
- isSplittingField_iff_intermediateFieldproof · cited by 2
- IntermediateField.adjoin_toSubalgebraproof · cited by 1
- IntermediateField.isSplittingField_iffproof · cited by 1
- IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRootproof · cited by 1
- Algebra.finite_of_essFiniteType_of_isAlgebraicproof · cited by 1
- Field.span_map_pow_expChar_pow_eq_top_of_isSeparableproof · cited by 0