Theorems · Definition · field theory
AlgebraicIndepOn
{ι : Type u_1} →
(R : Type u_3) → {A : Type u_5} → (ι → A) → [inst : CommRing R] → [inst_1 : CommRing A] → [Algebra R A] → Set ι → PropAlgebraicIndepOn R v s states that the elements in the family v that are indexed by the
elements of s are algebraically independent over R.
- Cited by
- 27 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Elemproof · cited by 7,166
- AlgebraicIndependentproof · cited by 120
Cited by30
Results whose statement or proof uses this declaration.
- IsTranscendenceBasisproof · cited by 74
- Algebra.trdegproof · cited by 39
- isTranscendenceBasis_equivproof · cited by 3
- isTranscendenceBasis_iff_of_subsingletonproof · cited by 3
- AlgebraicIndependent.isTranscendenceBasis_iff_isAlgebraicproof · cited by 3
- lift_trdeg_le_of_surjectiveproof · cited by 3
- trdeg_subsingletonproof · cited by 2
- IsTranscendenceBasis.of_compproof · cited by 2
- exists_isTranscendenceBasis_supersetstatement and proof · cited by 2
- AlgebraicIndepOn.insert_iffstatement and proof · cited by 2
- AlgebraicIndependent.iff_adjoin_imagestatement and proof · cited by 2
- lift_trdeg_le_of_injectiveproof · cited by 2