Theorems · Definition · group theory
Subsemigroup.center
(M : Type u_1) → [inst : Mul M] → Subsemigroup M
The center of a semigroup M is the set of elements that commute with everything in M
- Defined in
- Mathlib.GroupTheory.Subsemigroup.Center
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Mul
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.
- Subsemigroupstatement · cited by 323
- Set.centerproof · cited by 49
- Set.mul_mem_centerproof · cited by 1
Cited by45
Results whose statement or proof uses this declaration.
- NonUnitalSubsemiring.centerproof · cited by 22
- Subsemigroup.mem_center_iffstatement and proof · cited by 6
- Subsemigroup.centerCongrstatement and proof · cited by 2
- Subsemigroup.centerToMulOppositestatement and proof · cited by 2
- NonUnitalSubsemiring.centerCongrproof · cited by 2
- NonUnitalSubsemiring.centerToMulOppositeproof · cited by 2
- Subgroup.centerCongr_apply_coestatement and proof · cited by 1
- Subsemigroup.centerCongr_apply_coestatement and proof · cited by 0
- Subsemigroup.centerCongr_symm_apply_coestatement and proof · cited by 0
- Subsemigroup.centerToMulOpposite_apply_coestatement and proof · cited by 0
- Subsemigroup.centerToMulOpposite_symm_apply_coestatement and proof · cited by 0
- Subsemigroup.center_eq_topstatement and proof · cited by 0