Theorems · Theorem · group theory
IsMulCentral.comm
∀ {M : Type u_1} [inst : Mul M] {z : M}, IsMulCentral z → ∀ (a : M), Commute z amultiplication commutes
- Defined in
- Mathlib.Algebra.Group.Center
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Commutestatement · cited by 639
- IsMulCentralstatement and proof · cited by 13
Cited by26
Results whose statement or proof uses this declaration.
- Semigroup.mem_center_iffproof · cited by 12
- Set.centralizer_univproof · cited by 10
- Set.centralizer_eq_top_iff_subsetproof · cited by 8
- Set.center_subset_centralizerproof · cited by 8
- IsConj.eq_of_left_mem_centerproof · cited by 2
- IsMulCentral.mid_assocproof · cited by 1
- CompleteOrthogonalIdempotents.of_ker_isNilpotent_of_isMulCentralproof · cited by 1
- IsMulCentral.right_commproof · cited by 1
- Set.inv_mem_centerproof · cited by 1
- MulEquivClass.apply_mem_centerproof · cited by 1
- Subsemigroup.mem_corner_iff_mem_range_mul_leftproof · cited by 1
- Subsemigroup.mem_corner_iff_mul_leftproof · cited by 1