Theorems · Theorem · commutative algebra
IsScalarTower.adjoin_range_toAlgHom
∀ (R : Type u) (S : Type v) (A : Type w) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : CommSemiring A]
[inst_3 : Algebra R S] [inst_4 : Algebra S A] [inst_5 : Algebra R A] [inst_6 : IsScalarTower R S A] (t : Set A),
Subalgebra.restrictScalars R (Algebra.adjoin (↥(IsScalarTower.toAlgHom R S A).range) t) =
Subalgebra.restrictScalars R (Algebra.adjoin S t)- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Tower
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- IsScalarTowerstatement and proof · cited by 3,896
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- IsScalarTower.toAlgHomstatement and proof · cited by 232
- AlgHom.rangestatement and proof · cited by 169
- Subsemiring.closureproof · cited by 53
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.adjoin_eq_adjoin_unionproof · cited by 1
- Polynomial.IsSplittingField.mulproof · cited by 0