Theorems · Theorem · commutative algebra
smulAddHom_apply
∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (r : R) (x : M),
((smulAddHom R M) r) x = r • x- Defined in
- Mathlib.Algebra.Module.End
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement · cited by 3,230
- smulAddHomstatement · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Finsupp.toFreeAbelianGroup_comp_toFinsuppproof · cited by 1