Theorems · Theorem · field theory
Algebra.IsAlgebraic.injective_tower_top
∀ {R : Type u_1} (S : Type u_2) [inst : CommRing R] {A : Type u_3} [inst_1 : CommRing S] [NoZeroDivisors S]
[inst_3 : Algebra R S] [alg : Algebra.IsAlgebraic R S] [inst_4 : Ring A] [inst_5 : Algebra R A] [inst_6 : Algebra S A]
[IsScalarTower R S A], Function.Injective ⇑(algebraMap R A) → Function.Injective ⇑(algebraMap S A)- Defined in
- Mathlib.RingTheory.Algebraic.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- IsScalarTowerstatement and proof · cited by 3,896
- map_zeroproof · cited by 1,614
- NoZeroDivisorsstatement and proof · cited by 545
- Algebra.IsAlgebraicstatement and proof · cited by 322
- IsScalarTower.algebraMap_applyproof · cited by 116
- injective_iff_map_eq_zeroproof · cited by 62
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.extendScalarsproof · cited by 4
- Algebra.IsAlgebraic.faithfulSMul_tower_topproof · cited by 0