Theorems · Theorem · field theory
IsAlgebraic.tower_top
∀ {K : Type u_1} (L : Type u_2) {A : Type u_5} [inst : Field K] [inst_1 : Field L] [inst_2 : Ring A]
[inst_3 : Algebra K L] [inst_4 : Algebra L A] [inst_5 : Algebra K A] [IsScalarTower K L A] {x : A},
IsAlgebraic K x → IsAlgebraic L xIf x is algebraic over K, then x is algebraic over L when L is an extension of K
- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 113 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.
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- RingHom.injectiveproof · cited by 187
- IsAlgebraicstatement and proof · cited by 163
- IsAlgebraic.extendScalarsproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.sup_toSubalgebra_of_isAlgebraic_rightproof · cited by 6
- algebraicClosure.le_restrictScalarsproof · cited by 2
- Transcendental.of_tower_topproof · cited by 0