Theorems · Theorem · field theory
Algebra.injective_of_transcendental
∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A]
[h : Algebra.Transcendental R A], Function.Injective ⇑(algebraMap R A)- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 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 and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- Algebra.Transcendentalstatement and proof · cited by 17
- Algebra.transcendental_iff_not_isAlgebraicproof · cited by 8
- Algebra.isAlgebraic_of_not_injectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.TensorProduct.not_isField_of_transcendentalproof · cited by 1