Theorems · Definition · group theory
AddSubmonoid.center
(M : Type u_1) → [inst : AddZeroClass M] → AddSubmonoid M
The center of an addition with zero M is the set of elements that commute with everything in
M
- Defined in
- Mathlib.GroupTheory.Submonoid.Center
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement · cited by 1,178
- Set.addCenterproof · cited by 20
- Set.zero_mem_addCenterproof · cited by 0
Cited by20
Results whose statement or proof uses this declaration.
- AddSubgroup.centerproof · cited by 40
- AddSubmonoid.centerCongrstatement · cited by 2
- AddSubmonoid.centerToAddOppositestatement · cited by 2
- addUnitsCenterToCenterAddUnitsstatement and proof · cited by 2
- AddSubmonoid.coe_centerstatement · cited by 0
- AddSubmonoid.centerCongr_apply_coestatement · cited by 0
- val_addUnitsCenterToCenterAddUnits_apply_coestatement and proof · cited by 0
- AddSubmonoid.centerCongr_symm_apply_coestatement · cited by 0
- AddSubmonoid.centerToAddOpposite_apply_coestatement · cited by 0
- AddSubmonoid.centerToAddOpposite_symm_apply_coestatement · cited by 0
- AddSubmonoid.center_pistatement and proof · cited by 0
- AddSubmonoid.center_sumstatement and proof · cited by 0