Theorems · Theorem · commutative algebra
Algebra.adjoin_restrictScalars
∀ (C : Type u_1) (D : Type u_2) (E : Type u_3) [inst : CommSemiring C] [inst_1 : CommSemiring D]
[inst_2 : CommSemiring E] [inst_3 : Algebra C D] [inst_4 : Algebra C E] [inst_5 : Algebra D E]
[inst_6 : IsScalarTower C D E] (S : Set E),
Subalgebra.restrictScalars C (Algebra.adjoin D S) =
Subalgebra.restrictScalars C (Algebra.adjoin (↥(Subalgebra.map (IsScalarTower.toAlgHom C D E) ⊤)) S)- Defined in
- Mathlib.RingTheory.Adjoin.Tower
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- 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
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.FinitePresentation.of_restrict_scalars_finitePresentationproof · cited by 2
- Algebra.adjoin_res_eq_adjoin_resproof · cited by 0