Theorems · Theorem · ring theory
NonUnitalStarAlgebra.span_eq_toSubmodule
∀ {A : Type v} [inst : NonUnitalSemiring A] [inst_1 : StarRing A] {R : Type u_1} [inst_2 : CommSemiring R]
[inst_3 : Module R A] (s : NonUnitalStarSubalgebra R A), Submodule.span R ↑s = s.toSubmodule- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- StarRingstatement and proof · cited by 1,686
- Submodule.spanstatement · cited by 1,504
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalStarSubalgebrastatement and proof · cited by 196
- NonUnitalStarSubalgebra.toNonUnitalSubalgebrastatement · cited by 37
- NonUnitalSubalgebra.toSubmodulestatement · cited by 23
- Submodule.coe_span_eq_selfproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMap.adjoin_id_eq_span_one_unionproof · cited by 0