Theorems · Theorem · group theory
AddSemigroup.mem_center_iff
∀ {M : Type u_1} [inst : AddSemigroup M] {z : M}, z ∈ Set.addCenter M ↔ ∀ (g : M), g + z = z + g- Defined in
- Mathlib.Algebra.Group.Center
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- AddSemigroup
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.
- Setstatement · cited by 53,352
- add_assocproof · cited by 746
- AddSemigroupstatement and proof · cited by 136
- Set.addCenterstatement and proof · cited by 20
- IsAddCentral.commproof · cited by 10
Cited by9
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_center_iffproof · cited by 7
- Set.addCentralizer_eq_top_iff_subsetproof · cited by 3
- Set.addCentralizer_univproof · cited by 3
- Set.neg_mem_addCenterproof · cited by 1
- Set.addCenter_eq_univproof · cited by 1
- AddSubsemigroup.mem_center_iffproof · cited by 0
- AddSubmonoid.mem_center_iffproof · cited by 0
- Set.addUnits_neg_mem_centerproof · cited by 0
- Set.subset_addCenter_add_unitsproof · cited by 0