Theorems · Theorem · commutative algebra
DividedPowerAlgebra.LinearMap.dp_smul
∀ {R : Type u_2} {M : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (S : Type u_4)
[inst_3 : CommSemiring S] {N : Type u_5} [inst_4 : AddCommMonoid N] [inst_5 : Module R N] [inst_6 : Module S N]
(f : M →ₗ[R] N) [inst_7 : Algebra R S] [IsScalarTower R S N] {n : ℕ} {r : R} {a : M},
DividedPowerAlgebra.dp S n (f (r • a)) = r ^ n • DividedPowerAlgebra.dp S n (f a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- Finsuppstatement · cited by 5,255
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- MvPolynomialstatement · cited by 2,140
- map_powproof · cited by 503
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.