Theorems · Definition · group theory
nsmulAddMonoidHom
{α : Type u_1} → [inst : AddCommMonoid α] → ℕ → α →+ αMultiplication by a natural n on a commutative additive monoid,
considered as a morphism of additive monoids.
- Defined in
- Mathlib.Algebra.Group.Hom.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement · cited by 3,230
- nsmul_addproof · cited by 12
Cited by25
Results whose statement or proof uses this declaration.
- nsmulAddMonoidHom_applystatement and proof · cited by 9
- AddCommGroup.isAddTorsion_quotient_range_nsmulAddMonoidHomstatement and proof · cited by 2
- QuotientAddGroup.addEquivPiModRangeNSMulAddMonoidHomstatement and proof · cited by 2
- AddCommGroup.fg_of_descentstatement and proof · cited by 1
- Int.range_nsmulAddMonoidHomstatement · cited by 1
- IsAddCyclic.card_nsmulAddMonoidHom_kerstatement and proof · cited by 1
- AddSubgroup.isFiniteRelIndex_map_nsmulAddMonoidHom_of_fgstatement and proof · cited by 1
- IsAddCyclic.card_nsmulAddMonoidHom_rangestatement and proof · cited by 1
- IsAddCyclic.index_nsmulAddMonoidHom_kerstatement and proof · cited by 1
- AddCircle.isAddQuotientCoveringMap_nsmulstatement and proof · cited by 1
- AddSubgroup.index_range_nsmulstatement and proof · cited by 1
- AddSubgroup.addSubgroupOf_map_nsmulAddMonoidHom_eq_rangestatement · cited by 1