Theorems · Theorem · ring theory
Unitization.starLift_range_le
∀ {R : Type u_1} {A : Type u_2} {C : Type u_3} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A]
[inst_2 : StarRing R] [inst_3 : StarRing A] [inst_4 : Module R A] [inst_5 : SMulCommClass R A A]
[inst_6 : IsScalarTower R A A] [inst_7 : StarModule R A] [inst_8 : Semiring C] [inst_9 : StarRing C]
[inst_10 : Algebra R C] [inst_11 : StarModule R C] {f : A →⋆ₙₐ[R] C} {S : StarSubalgebra R C},
(Unitization.starLift f).range ≤ S ↔ NonUnitalStarAlgHom.range f ≤ S.toNonUnitalStarSubalgebra- Cited by
- 1 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Equivstatement · cited by 8,337
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
Cited by1
Results whose statement or proof uses this declaration.
- Unitization.starLift_rangeproof · cited by 1