Theorems · Theorem · ring theory
NonUnitalStarSubalgebra.toNonUnitalSubalgebra_le_iff
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A] [inst_2 : Module R A]
[inst_3 : Star A] {S₁ S₂ : NonUnitalStarSubalgebra R A}, S₁.toNonUnitalSubalgebra ≤ S₂.toNonUnitalSubalgebra ↔ S₁ ≤ S₂- Defined in
- Mathlib.Algebra.Star.NonUnitalSubalgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Starstatement and proof · cited by 496
- NonUnitalSubalgebrastatement · cited by 215
- NonUnitalStarSubalgebrastatement and proof · cited by 196
- NonUnitalStarSubalgebra.toNonUnitalSubalgebrastatement · cited by 37
Cited by3
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgebra.gcproof · cited by 3
- NonUnitalSubalgebra.starClosure_leproof · cited by 2
- NonUnitalStarAlgebra.adjoin_le_centralizer_centralizerproof · cited by 2