Theorems · Theorem · field theory
AlgebraicIndependent.extendScalars_of_isIntegral
∀ {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 → ∀ [Algebra.IsIntegral R S], AlgebraicIndependent S x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 142 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- IsScalarTowerstatement and proof · cited by 3,896
- Nontrivialproof · cited by 2,416
- NoZeroDivisorsstatement and proof · cited by 545
- Algebra.IsIntegralstatement and proof · cited by 224
- AlgebraicIndependentstatement and proof · cited by 120
- Module.nontrivialproof · cited by 17
- AlgebraicIndependent.extendScalarsproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.IsIntegral.algebraicIndependent_iffproof · cited by 1
- AlgebraicIndependent.integralClosureproof · cited by 0