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Theorems · Definition · ring theory

NonUnitalStarSubalgebra.centralizer

(R : Type u) →
  {A : Type v} →
    [inst : CommSemiring R] →
      [inst_1 : NonUnitalSemiring A] →
        [inst_2 : StarRing A] →
          [inst_3 : Module R A] → [IsScalarTower R A A] → [SMulCommClass R A A] → Set A → NonUnitalStarSubalgebra R A

The centralizer of the star-closure of a set as a non-unital star subalgebra.

Defined in
Mathlib.Algebra.Star.NonUnitalSubalgebra
Cited by
11 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringNonUnitalSemiringStarRingModuleIsScalarTowerSMulCommClass

Around this declaration

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

NonUnitalStarSubalgebra.coe_centralizer · cited by 2NonUnitalStarSubalgebra.c…NonUnitalStarAlgebra.adjoin_le_centralizer_centralizer · cited by 2NonUnitalStarAlgebra.adjo…NonUnitalStarSubalgebra.centralizer_toNonUnitalSubalgebra · cited by 1NonUnitalStarSubalgebra.c…NonUnitalStarSubalgebra.coe_centralizer_centralizer · cited by 1NonUnitalStarSubalgebra.c…NonUnitalStarAlgebra.isMulCommutative_adjoin · cited by 1NonUnitalStarAlgebra.isMu…NonUnitalStarSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer · cited by 1NonUnitalStarSubalgebra.t…NonUnitalStarSubalgebra.centralizer_le · cited by 0NonUnitalStarSubalgebra.c…NonUnitalStarSubalgebra.centralizer_univ · cited by 0NonUnitalStarSubalgebra.c…NonUnitalStarAlgebra.elemental.le_centralizer_centralizer · cited by 0elemental.le_centralizer_…NonUnitalStarSubalgebra.mem_centralizer_iff · cited by 0NonUnitalStarSubalgebra.m…NonUnitalStarSubalgebra.centralizer.congr_simp · cited by 0centralizer.congr_simpSet · cited by 53352SetModule · cited by 20661ModuleCommSemiring · cited by 10911CommSemiringIsScalarTower · cited by 3896IsScalarTowerSMulCommClass · cited by 1927SMulCommClassStarRing · cited by 1686StarRingStar.star · cited by 1082Star.starNonUnitalSemiring · cited by 339NonUnitalSemiringNonUnitalSubalgebra · cited by 215NonUnitalSubalgebraNonUnitalStarSubalgebra · cited by 196NonUnitalStarSubalgebraNonUnitalSubalgebra.centralizer · cited by 12NonUnitalSubalgebra.centr…NonUnitalStarSubalgebra.centr…CITED BYCITES

Cites11

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

Cited by11

Results whose statement or proof uses this declaration.