Theorems · Theorem · field theory
algebraicIndependent_iff
∀ {ι : Type u_1} {R : Type u_3} {A : Type u_5} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A]
[inst_2 : Algebra R A], AlgebraicIndependent R x ↔ ∀ (p : MvPolynomial ι R), (MvPolynomial.aeval x) p = 0 → p = 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 96 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.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Finsuppstatement · cited by 5,255
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement · cited by 2,140
- MvPolynomial.aevalstatement and proof · cited by 298
- AlgebraicIndependentstatement · cited by 120
- injective_iff_map_eq_zeroproof · cited by 62
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.of_subsingletonproof · cited by 2
- AlgebraicIndependent.of_ringHom_of_comp_eqproof · cited by 1
- AlgebraicIndependent.ringHom_of_comp_eqproof · cited by 1
- AlgebraicIndependent.aeval_of_algebraicIndependentproof · cited by 1
- AlgebraicIndependent.of_aevalproof · cited by 0
- AlgebraicIndependent.eq_zero_of_aeval_eq_zeroproof · cited by 0