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 AReinterpret a NonUnitalSubalgebra as a Submodule.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement · cited by 7,192
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- NonUnitalSubalgebrastatement and proof · cited by 215
- NonUnitalSubsemiring.toAddSubmonoidproof · cited by 56
- NonUnitalSubalgebra.toNonUnitalSubsemiringproof · cited by 33
- NonUnitalSubalgebra.smul_mem'proof · cited by 4
Cited by26
Results whose statement or proof uses this declaration.
- NonUnitalSubalgebra.topologicalClosureproof · cited by 8
- NonUnitalAlgebra.gcproof · cited by 5
- NonUnitalAlgebra.adjoin_eq_spanstatement and proof · cited by 2
- StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_spanstatement and proof · cited by 2
- NonUnitalSubalgebra.toSubmodule_injectivestatement and proof · cited by 1
- NonUnitalStarAlgebra.span_eq_toSubmodulestatement · cited by 1
- NonUnitalStarAlgebra.adjoin_eq_spanstatement and proof · cited by 1
- NonUnitalSubalgebra.map_toSubmodulestatement and proof · cited by 0
- NonUnitalSubalgebra.toSubmodule'proof · cited by 0
- NonUnitalSubalgebra.toSubmoduleEquivstatement and proof · cited by 0
- NonUnitalSubalgebra.toSubmodule_injstatement · cited by 0
- NonUnitalAlgebra.sInf_toSubmodulestatement and proof · cited by 0