Theorems · Theorem · commutative algebra
Algebra.Generators.map_ofComp_ker
∀ {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),
Ideal.map (Q.ofComp P).toAlgHom (Q.comp P).ker = Q.ker- Defined in
- Mathlib.RingTheory.Extension.Generators
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 105 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.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Finsuppstatement · cited by 5,255
- Idealstatement · cited by 4,748
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement · cited by 3,236
- Ideal.mapstatement · cited by 692
- MvPolynomial.aevalproof · cited by 298
- Algebra.Generatorsstatement and proof · cited by 152
- Algebra.Generators.Ringstatement and proof · cited by 133
- Ideal.extproof · cited by 131
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.Generators.Cotangent.exactproof · cited by 6
- Algebra.Generators.Cotangent.surjective_map_ofCompproof · cited by 3
- Algebra.Generators.ker_comp_eq_supproof · cited by 1