Theorems · Theorem · ring theory
Unitization.lift_range
∀ {R : Type u_1} {A : Type u_2} {C : Type u_3} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A]
[inst_2 : Module R A] [inst_3 : SMulCommClass R A A] [inst_4 : IsScalarTower R A A] [inst_5 : Semiring C]
[inst_6 : Algebra R C] (f : A →ₙₐ[R] C), (Unitization.lift f).range = Algebra.adjoin R ↑(NonUnitalAlgHom.range f)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- SetLike.coestatement and proof · cited by 8,199
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement · cited by 3,236
- SMulCommClassstatement and proof · cited by 1,927
- Subalgebrastatement and proof · cited by 1,353
- Algebra.adjoinstatement and proof · cited by 535
Cited by1
Results whose statement or proof uses this declaration.
- NonUnitalSubalgebra.unitization_rangeproof · cited by 2