Theorems · Theorem · ring theory
StarSubalgebra.inclusion_injective
∀ {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} (h : S₁ ≤ S₂),
Function.Injective ⇑(StarSubalgebra.inclusion h)- Defined in
- Mathlib.Algebra.Star.Subalgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- StarModulestatement and proof · cited by 570
- StarAlgHomstatement · cited by 215
- StarSubalgebrastatement and proof · cited by 194
- Set.inclusion_injectiveproof · cited by 28
- StarSubalgebra.inclusionstatement · cited by 9
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.