Theorems · Theorem · commutative algebra
Subalgebra.restrictScalars_injective
∀ (R : Type u) {S : Type v} {A : Type w} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Semiring A]
[inst_3 : Algebra R S] [inst_4 : Algebra S A] [inst_5 : Algebra R A] [inst_6 : IsScalarTower R S A],
Function.Injective (Subalgebra.restrictScalars R)- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Tower
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 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
- Subalgebrastatement and proof · cited by 1,353
- Subalgebra.restrictScalarsstatement and proof · cited by 36
- Subalgebra.extproof · cited by 28
- Subalgebra.mem_restrictScalarsproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraicproof · cited by 5
- Algebra.FinitePresentation.of_restrict_scalars_finitePresentationproof · cited by 2