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Theorems · Definition · nonassociative algebras

NonUnitalSubalgebra.centralizer

(R : Type u_1) →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : NonUnitalSemiring A] →
        [inst_2 : Module R A] → [IsScalarTower R A A] → [SMulCommClass R A A] → Set A → NonUnitalSubalgebra R A

The centralizer of a set as a non-unital subalgebra.

Defined in
Mathlib.Algebra.Algebra.NonUnitalSubalgebra
Cited by
12 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringNonUnitalSemiringModuleIsScalarTowerSMulCommClass

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NonUnitalStarSubalgebra.centralizer · cited by 11NonUnitalStarSubalgebra.c…NonUnitalAlgebra.adjoin_le_centralizer_centralizer · cited by 4NonUnitalAlgebra.adjoin_l…NonUnitalAlgebra.commute_of_mem_adjoin_of_forall_mem_commute · cited by 2NonUnitalAlgebra.commute_…NonUnitalStarAlgebra.adjoin_le_centralizer_centralizer · cited by 2NonUnitalStarAlgebra.adjo…NonUnitalStarSubalgebra.centralizer_toNonUnitalSubalgebra · cited by 1NonUnitalStarSubalgebra.c…NonUnitalSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer · cited by 1NonUnitalSubalgebra.topol…NonUnitalSubalgebra.centralizer_le · cited by 0NonUnitalSubalgebra.centr…NonUnitalSubalgebra.centralizer_univ · cited by 0NonUnitalSubalgebra.centr…NonUnitalSubalgebra.coe_centralizer · cited by 0NonUnitalSubalgebra.coe_c…NonUnitalSubalgebra.centralizer.congr_simp · cited by 0centralizer.congr_simpNonUnitalAlgebra.elemental.le_centralizer_centralizer · cited by 0elemental.le_centralizer_…NonUnitalSubalgebra.mem_centralizer_iff · cited by 0NonUnitalSubalgebra.mem_c…NonUnitalAlgebra.isMulCommutative_adjoin · cited by 0NonUnitalAlgebra.isMulCom…Set · cited by 53352SetModule · cited by 20661ModuleCommSemiring · cited by 10911CommSemiringIsScalarTower · cited by 3896IsScalarTowerSMulCommClass · cited by 1927SMulCommClassNonUnitalSemiring · cited by 339NonUnitalSemiringNonUnitalSubalgebra · cited by 215NonUnitalSubalgebraNonUnitalSubsemiring · cited by 201NonUnitalSubsemiringNonUnitalSubsemiring.centralizer · cited by 10NonUnitalSubsemiring.cent…Set.smul_mem_centralizer · cited by 0Set.smul_mem_centralizerNonUnitalSubalgebra.centraliz…CITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by13

Results whose statement or proof uses this declaration.