Theorems · Theorem · commutative algebra
Submodule.restrictScalars_injective
∀ (S : Type u_1) (R : Type u_2) (M : Type u_3) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Semiring S] [inst_3 : Module S M] [inst_4 : Module R M] [inst_5 : SMul S R] [inst_6 : IsScalarTower S R M], Function.Injective (Submodule.restrictScalars S)
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, 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.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- Submodule.extproof · cited by 204
- Submodule.restrictScalarsstatement and proof · cited by 180
- Set.ext_iffproof · cited by 90
- SetLike.ext'_iffproof · cited by 78
Cited by9
Results whose statement or proof uses this declaration.
- Submodule.restrictScalarsEmbeddingproof · cited by 5
- Submodule.restrictScalars_injproof · cited by 5
- Submodule.FG.of_restrictScalarsproof · cited by 2
- exists_subalgebra_of_fgproof · cited by 1
- Submodule.localized'_smulproof · cited by 1
- MvPolynomial.pow_idealOfVarsproof · cited by 1
- Module.Finite.rightproof · cited by 1
- TensorProduct.AlgebraTensorModule.range_lTensor_idealMapproof · cited by 0
- IsLocalRing.CotangentSpace.span_image_eq_top_iffproof · cited by 0