Theorems · Theorem · commutative algebra
AlgHom.restrictScalars_injective
∀ (R : Type u) {S : Type v} {A : Type w} {B : Type u₁} [inst : CommSemiring R] [inst_1 : CommSemiring S]
[inst_2 : Semiring A] [inst_3 : Semiring B] [inst_4 : Algebra R S] [inst_5 : Algebra S A] [inst_6 : Algebra S B]
[inst_7 : Algebra R A] [inst_8 : Algebra R B] [inst_9 : IsScalarTower R S A] [inst_10 : IsScalarTower R S B],
Function.Injective (AlgHom.restrictScalars R)- Defined in
- Mathlib.Algebra.Algebra.Tower
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- AlgHom.extproof · cited by 170
- AlgHom.restrictScalarsstatement and proof · cited by 83
- AlgHom.congr_funproof · cited by 40
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.of_restrictScalarsproof · cited by 9
- Field.primitive_element_iff_algHom_eq_of_evalproof · cited by 1