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Theorems · Definition · ring theory

NonUnitalStarSubalgebra.toNonUnitalSubalgebra

{R : Type u} →
  {A : Type v} →
    [inst : CommSemiring R] →
      [inst_1 : NonUnitalNonAssocSemiring A] →
        [inst_2 : Module R A] → [inst_3 : Star A] → NonUnitalStarSubalgebra R A → NonUnitalSubalgebra R A

Reinterpret a NonUnitalStarSubalgebra as a NonUnitalSubalgebra.

Defined in
Mathlib.Algebra.Star.NonUnitalSubalgebra
Cited by
37 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CommSemiringNonUnitalNonAssocSemiringModuleStar
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Around this declaration

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

NonUnitalStarSubalgebra.map · cited by 23NonUnitalStarSubalgebra.m…NonUnitalStarSubalgebra.topologicalClosure · cited by 12NonUnitalStarSubalgebra.t…NonUnitalStarSubalgebra.prod · cited by 7NonUnitalStarSubalgebra.p…NonUnitalStarSubalgebra.comap · cited by 5NonUnitalStarSubalgebra.c…NonUnitalStarAlgHom.codRestrict · cited by 5NonUnitalStarAlgHom.codRe…NonUnitalStarSubalgebra.toNonUnitalSubring · cited by 4NonUnitalStarSubalgebra.t…NonUnitalStarSubalgebra.toNonUnitalSubalgebra_injective · cited by 3NonUnitalStarSubalgebra.t…NonUnitalStarSubalgebra.toNonUnitalSubalgebra_le_iff · cited by 3NonUnitalStarSubalgebra.t…NonUnitalStarSubalgebra.copy · cited by 3NonUnitalStarSubalgebra.c…NonUnitalStarAlgebra.adjoin_toNonUnitalSubalgebra · cited by 3NonUnitalStarAlgebra.adjo…NonUnitalStarAlgebra.gc · cited by 3NonUnitalStarAlgebra.gcNonUnitalStarSubalgebra.toStarSubalgebra · cited by 2NonUnitalStarSubalgebra.t…NonUnitalStarSubalgebra.coe_iSup_of_directed · cited by 2NonUnitalStarSubalgebra.c…NonUnitalSubalgebra.starClosure_le · cited by 2NonUnitalSubalgebra.starC…NonUnitalStarAlgebra.adjoin_le_centralizer_centralizer · cited by 2NonUnitalStarAlgebra.adjo…Module · cited by 20661ModuleCommSemiring · cited by 10911CommSemiringNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringStar · cited by 496StarNonUnitalSubalgebra · cited by 215NonUnitalSubalgebraNonUnitalStarSubalgebra · cited by 196NonUnitalStarSubalgebraNonUnitalStarSubalgebra.toNon…CITED BYCITES

Cites6

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

Cited by47

Results whose statement or proof uses this declaration.