Theorems · Theorem · field theory
algebraicIndependent_empty_iff
∀ (R : Type u_2) (A : Type v) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A], AlgebraicIndependent R Subtype.val ↔ Function.Injective ⇑(algebraMap R A)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgebraicIndependentstatement · cited by 120
Cited by2
Results whose statement or proof uses this declaration.
- exists_isTranscendenceBasisproof · cited by 5
- exists_isTranscendenceBasis_subsetproof · cited by 2