Theorems · Theorem · commutative algebra
RingHom.ker_equiv_comp
∀ {R : Type u} {S : Type v} {T : Type w} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : Semiring T] (f : R →+* S)
(e : S ≃+* T), RingHom.ker (e.toRingHom.comp f) = RingHom.ker f- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- RingEquivstatement and proof · cited by 1,147
- RingHom.compstatement · cited by 899
- Ideal.comapproof · cited by 443
- RingHom.kerstatement and proof · cited by 363
- RingEquiv.toRingHomstatement and proof · cited by 150
- RingHom.comap_kerproof · cited by 16
- RingHom.ker_coe_equivproof · cited by 6
- RingEquiv.toRingHom_eq_coeproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.ker_subschemeι_appproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.ker_glueDataObjι_appTopproof · cited by 1
- AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_compproof · cited by 0