Theorems · Theorem · ring theory
NonUnitalStarAlgebra.toNonUnitalSubalgebra_eq_top
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : NonUnitalSemiring A]
[inst_3 : StarRing A] [inst_4 : Module R A] [inst_5 : IsScalarTower R A A] [inst_6 : SMulCommClass R A A]
[inst_7 : StarModule R A] {S : NonUnitalStarSubalgebra R A}, S.toNonUnitalSubalgebra = ⊤ ↔ S = ⊤- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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
- Top.topstatement · cited by 9,680
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalSubalgebrastatement · cited by 215
- NonUnitalStarSubalgebrastatement and proof · cited by 196
- NonUnitalStarSubalgebra.toNonUnitalSubalgebrastatement · cited by 37
- NonUnitalStarSubalgebra.toNonUnitalSubalgebra_injectiveproof · cited by 3
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