Theorems · Theorem · commutative algebra
Algebra.adjoin_algebraMap
∀ (R : Type uR) {S : Type uS} (A : Type uA) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Semiring A]
[inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [inst_6 : IsScalarTower R S A] (s : Set S),
Algebra.adjoin R (⇑(algebraMap S A) '' s) = Subalgebra.map (IsScalarTower.toAlgHom R S A) (Algebra.adjoin R s)- Defined in
- Mathlib.RingTheory.Adjoin.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Set.imagestatement · cited by 5,609
- Algebra.algebraMapstatement · cited by 4,706
- 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 by3
Results whose statement or proof uses this declaration.
- Algebra.adjoin_algebraMap_image_union_eq_adjoin_adjoinproof · cited by 3
- Algebra.FinitePresentation.of_restrict_scalars_finitePresentationproof · cited by 2
- Polynomial.IsSplittingField.mulproof · cited by 0