Theorems · Definition · group theory
addUnitsCenterToCenterAddUnits
(M : Type u_1) → [inst : AddMonoid M] → AddUnits ↥(AddSubmonoid.center M) →+ ↥(AddSubmonoid.center (AddUnits M))
For an additive monoid, the units of the center inject into the center of the units.
- Defined in
- Mathlib.GroupTheory.Submonoid.Center
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidHomstatement · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement · cited by 1,178
- AddUnitsstatement and proof · cited by 325
- AddSubmonoid.subtypeproof · cited by 28
- AddUnits.mapproof · cited by 16
- AddSubmonoid.centerstatement and proof · cited by 15
- AddMonoidHom.codRestrictproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- val_addUnitsCenterToCenterAddUnits_apply_coestatement and proof · cited by 0
- addUnitsCenterToCenterAddUnits_injectivestatement and proof · cited by 0