Theorems · Theorem · field theory
AlgebraicIndependent.extendScalars
∀ {ι : Type u_1} {R : Type u_2} {A : Type u_4} {x : ι → A} (S : Type u_5) [inst : CommRing R] [inst_1 : CommRing S]
[inst_2 : CommRing A] [inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [IsScalarTower R S A]
[NoZeroDivisors S], AlgebraicIndependent R x → ∀ [alg : Algebra.IsAlgebraic R S], AlgebraicIndependent S x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Elemproof · cited by 7,166
- Set.imageproof · cited by 5,609
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Nontrivialproof · cited by 2,416
- Set.Finiteproof · cited by 1,814
- map_zeroproof · cited by 1,614
- Subalgebraproof · cited by 1,353
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.extendScalars_of_isIntegralproof · cited by 2
- Algebra.IsAlgebraic.algebraicIndependent_iffproof · cited by 2
- AlgebraicIndependent.algebraicClosureproof · cited by 0
- AlgebraicIndependent.subalgebraAlgebraicClosureproof · cited by 0