Theorems · Theorem · ring theory
StarSubalgebra.toSubalgebra_le_iff
∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
[inst_3 : StarRing A] [inst_4 : Algebra R A] [inst_5 : StarModule R A] {S₁ S₂ : StarSubalgebra R A},
S₁.toSubalgebra ≤ S₂.toSubalgebra ↔ S₁ ≤ S₂- Defined in
- Mathlib.Algebra.Star.Subalgebra
- 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- StarRingstatement and proof · cited by 1,686
- Subalgebrastatement · cited by 1,353
- StarModulestatement and proof · cited by 570
- StarSubalgebrastatement and proof · cited by 194
- StarSubalgebra.toSubalgebrastatement · cited by 58
Cited by3
Results whose statement or proof uses this declaration.
- StarAlgebra.gcproof · cited by 4
- StarAlgebra.adjoin_le_centralizer_centralizerproof · cited by 2
- Subalgebra.starClosure_leproof · cited by 1