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Theorems · Definition · nonassociative algebras

NonUnitalSubalgebra.toSubmodule

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

Reinterpret a NonUnitalSubalgebra as a Submodule.

Defined in
Mathlib.Algebra.Algebra.NonUnitalSubalgebra
Cited by
23 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
CommSemiringNonUnitalNonAssocSemiringModule

Around this declaration

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

NonUnitalSubalgebra.topologicalClosure · cited by 8NonUnitalSubalgebra.topol…NonUnitalAlgebra.gc · cited by 5NonUnitalAlgebra.gcNonUnitalAlgebra.adjoin_eq_span · cited by 2NonUnitalAlgebra.adjoin_e…StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_span · cited by 2StarAlgebra.adjoin_nonUni…NonUnitalSubalgebra.toSubmodule_injective · cited by 1NonUnitalSubalgebra.toSub…NonUnitalStarAlgebra.span_eq_toSubmodule · cited by 1NonUnitalStarAlgebra.span…NonUnitalStarAlgebra.adjoin_eq_span · cited by 1NonUnitalStarAlgebra.adjo…NonUnitalSubalgebra.map_toSubmodule · cited by 0NonUnitalSubalgebra.map_t…NonUnitalSubalgebra.toSubmodule' · cited by 0NonUnitalSubalgebra.toSub…NonUnitalSubalgebra.toSubmoduleEquiv · cited by 0NonUnitalSubalgebra.toSub…NonUnitalSubalgebra.toSubmodule_inj · cited by 0NonUnitalSubalgebra.toSub…NonUnitalAlgebra.sInf_toSubmodule · cited by 0NonUnitalAlgebra.sInf_toS…NonUnitalAlgebra.span_eq_toSubmodule · cited by 0NonUnitalAlgebra.span_eq_…NonUnitalSubalgebra.toSubmodule_toNonUnitalSubalgebra · cited by 0NonUnitalSubalgebra.toSub…ContinuousMap.adjoin_id_eq_span_one_union · cited by 0ContinuousMap.adjoin_id_e…Module · cited by 20661ModuleCommSemiring · cited by 10911CommSemiringSubmodule · cited by 7192SubmoduleNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringNonUnitalSubalgebra · cited by 215NonUnitalSubalgebraNonUnitalSubsemiring.toAddSubmonoid · cited by 56NonUnitalSubsemiring.toAd…NonUnitalSubalgebra.toNonUnitalSubsemiring · cited by 33NonUnitalSubalgebra.toNon…NonUnitalSubalgebra.smul_mem' · cited by 4NonUnitalSubalgebra.smul_…NonUnitalSubalgebra.toSubmodu…CITED BYCITES

Cites8

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

Cited by26

Results whose statement or proof uses this declaration.