Theorems · Theorem · commutative algebra
Algebra.Generators.ofComp_kerCompPreimage
∀ {R : Type u} {S : Type v} {ι : Type w} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
{ι' : Type u_3} {T : Type u_7} [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T]
[inst_6 : IsScalarTower R S T] (Q : Algebra.Generators S T ι') (P : Algebra.Generators R S ι) (x : ↥Q.ker),
(Q.ofComp P).toAlgHom ↑(Q.kerCompPreimage P x) = ↑x- Defined in
- Mathlib.RingTheory.Extension.Generators
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites53
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Finsuppstatement and proof · cited by 5,255
- Finset.sumproof · cited by 5,195
- Idealstatement · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- Finset.sum_congrproof · cited by 2,323
- MvPolynomialproof · cited by 2,140
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.Generators.H1Cotangent.δ_eq_δAuxproof · cited by 3
- Algebra.Generators.map_ofComp_kerproof · cited by 3