Theorems · Definition · group theory
zsmulAddGroupHom
{α : Type u_1} → [inst : SubtractionCommMonoid α] → ℤ → α →+ αMultiplication by an integer n on a commutative additive group,
considered as an additive group homomorphism.
- Defined in
- Mathlib.Algebra.Group.Hom.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- SubtractionCommMonoid
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.
- AddMonoidHomstatement · cited by 3,230
- SubtractionCommMonoidstatement and proof · cited by 79
- zsmul_addproof · cited by 3
Cited by15
Results whose statement or proof uses this declaration.
- QuotientAddGroup.equivQuotientZSMulOfEquivstatement · cited by 3
- QuotientAddGroup.homQuotientZSMulOfHomstatement and proof · cited by 3
- zsmulAddGroupHom_applystatement and proof · cited by 2
- AddCircle.isAddQuotientCoveringMap_zsmulstatement · cited by 2
- Multiset.sum_map_zsmulproof · cited by 1
- vadd_eq_self_of_preimage_zsmul_eq_selfproof · cited by 1
- AddCircle.isAddQuotientCoveringMap_nsmulproof · cited by 1
- QuotientAddGroup.equivQuotientZSMulOfEquiv_reflstatement and proof · cited by 0
- DistribSMul.toAddMonoidHom_eq_zsmulAddGroupHomstatement · cited by 0
- QuotientAddGroup.equivQuotientZSMulOfEquiv_symmstatement · cited by 0
- QuotientAddGroup.equivQuotientZSMulOfEquiv_transstatement and proof · cited by 0
- QuotientAddGroup.homQuotientZSMulOfHom_compstatement and proof · cited by 0