Theorems · Theorem · commutative algebra
IsScalarTower.algebraMap_smul
∀ {R : Type u} (A : Type w) {M : Type v₁} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : MulAction A M] [inst_4 : SMul R M] [IsScalarTower R A M] (r : R) (x : M), (algebraMap R A) r • x = r • x- Defined in
- Mathlib.Algebra.Algebra.Tower
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- one_smulproof · cited by 1,374
- MulActionstatement and proof · cited by 1,294
- Algebra.algebraMap_eq_smul_oneproof · cited by 119
- IsScalarTower.smul_assocproof · cited by 10
Cited by19
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.dualSubmodule_span_of_basisproof · cited by 7
- IsBaseChange.basis_repr_comp_applyproof · cited by 3
- MvPowerSeries.prod_smul_X_eq_smul_monomial_oneproof · cited by 2
- RootPairing.rootFormIn_self_smul_corootproof · cited by 2
- Algebra.pow_smul_mem_of_smul_subset_of_mem_adjoinproof · cited by 2
- Algebra.Generators.H1Cotangent.δAux_ofCompproof · cited by 1
- Algebra.Generators.H1Cotangent.δAux_toAlgHomproof · cited by 1
- IsLocalization.integerNormalization_eval₂_eq_zeroproof · cited by 1
- star_mul_self_sub_self_mul_starproof · cited by 1
- Ideal.FinrankQuotientMap.linearIndependent_of_nontrivialproof · cited by 1
- IsLocalization.mem_span_iffproof · cited by 1
- trace_eq_sum_rootsproof · cited by 1