Theorems · Definition · commutative algebra
zmultiplesHom
(β : Type u_4) → [inst : AddGroup β] → β ≃ (ℤ →+ β)
Additive homomorphisms from ℤ are defined by the image of 1.
- Defined in
- Mathlib.Data.Int.Cast.Lemmas
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equivstatement · cited by 8,337
- AddGroupstatement and proof · cited by 4,410
- AddMonoidHomstatement and proof · cited by 3,230
- add_zsmulproof · cited by 21
Cited by14
Results whose statement or proof uses this declaration.
- zpowersHomproof · cited by 9
- zmodAddEquivOfGeneratorproof · cited by 5
- intEquivOfZMultiplesEqTopproof · cited by 4
- uliftZMultiplesHomproof · cited by 4
- AddCommGrpCat.asHomproof · cited by 3
- zmultiplesAddHomproof · cited by 2
- zmultiplesHom_ker_eqstatement and proof · cited by 2
- zmultiplesHom_symm_applystatement · cited by 1
- AddAction.zmultiplesQuotientStabilizerEquivproof · cited by 1
- zmultiplesHom_applystatement · cited by 1
- AddSubgroup.range_zmultiplesHomstatement · cited by 1
- AddMonoidHom.apply_intproof · cited by 0