Theorems · Theorem · commutative algebra
RingHom.ker_eq
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S]
[rcf : RingHomClass F R S] (f : F), ↑(RingHom.ker f) = ⇑f ⁻¹' {0}- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- SetLike.coestatement · cited by 8,199
- Set.preimagestatement · cited by 4,946
- Idealstatement · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- RingHom.kerstatement · cited by 363
- RingHomClassstatement and proof · cited by 193
Cited by1
Results whose statement or proof uses this declaration.
- RingHom.injective_iff_ker_eq_botproof · cited by 29