Theorems · Theorem · ring theory
AlgHom.map_smul_of_tower
∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] (φ : A →ₐ[R] B) {R' : Type u_1} [inst_5 : SMul R' A]
[inst_6 : SMul R' B] [LinearMap.CompatibleSMul A B R' R] (r : R') (x : A), φ (r • x) = r • φ x- Defined in
- Mathlib.Algebra.Algebra.Hom
- Cited by
- 7 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.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement and proof · cited by 3,236
- AlgHom.toLinearMapproof · cited by 254
- LinearMap.CompatibleSMulstatement and proof · cited by 86
- LinearMap.map_smul_of_towerproof · cited by 50
Cited by7
Results whose statement or proof uses this declaration.
- PowerSeries.subst_smulproof · cited by 1
- groupCohomology.exists_mul_galRestrict_of_norm_eq_oneproof · cited by 0
- PowerSeries.expand_smulproof · cited by 0
- IsStronglyTranscendental.of_isLocalization_leftproof · cited by 0
- MvPowerSeries.expand_Cproof · cited by 0
- MvPowerSeries.subst_smulproof · cited by 0
- PowerSeries.expand_Cproof · cited by 0