Theorems · Theorem · commutative algebra
AlgHom.comap_ker
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] {C : Type u_4} [inst_5 : Semiring C] [inst_6 : Algebra R C]
(f : B →ₐ[R] C) (g : A →ₐ[R] B), Ideal.comap g (RingHom.ker f) = RingHom.ker (f.comp g)- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement · cited by 4,748
- AlgHomstatement and proof · cited by 3,236
- AlgHom.compstatement · cited by 501
- AlgHom.toRingHomproof · cited by 490
- Ideal.comapstatement · cited by 443
- RingHom.kerstatement · cited by 363
- RingHom.comap_kerproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.Presentation.span_range_relation_eq_ker_compproof · cited by 0
- Algebra.Generators.ker_ofAlgEquivproof · cited by 0