Theorems · Theorem · ring theory
Module.End.smulLeft_apply
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (α : R)
(hα : α ∈ Set.center R) (x : M), (Module.End.smulLeft α hα) x = α • x- Defined in
- Mathlib.Algebra.Module.LinearMap.End
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
- Assumes
- SemiringAddCommMonoidModule
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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Set.centerstatement and proof · cited by 49
- Module.End.smulLeftstatement and proof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.mem_center_iffproof · cited by 4