Theorems · Theorem · field theory
algebraicIndependent_comp_subtype
∀ {ι : Type u} {R : Type u_2} {A : Type v} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
{s : Set ι},
AlgebraicIndependent R (x ∘ Subtype.val) ↔ ∀ p ∈ MvPolynomial.supported R s, (MvPolynomial.aeval x) p = 0 → p = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Elemstatement and proof · cited by 7,166
- Finsuppstatement · cited by 5,255
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- Subalgebrastatement · cited by 1,353
- AlgHom.compproof · cited by 501
- AlgHom.toRingHomproof · cited by 490
- MvPolynomial.aevalstatement and proof · cited by 298
Cited by2
Results whose statement or proof uses this declaration.
- algebraicIndependent_of_finite_typeproof · cited by 1
- algebraicIndependent_subtypeproof · cited by 1