Theorems · Theorem · commutative algebra
Pi.ker_ringHom
∀ {S : Type v} [inst : Semiring S] {ι : Type u_3} {R : ι → Type u_4} [inst_1 : (i : ι) → Semiring (R i)]
(φ : (i : ι) → S →+* R i), RingHom.ker (RingHom.pi φ) = ⨅ i, RingHom.ker (φ i)- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, 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.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Idealstatement · cited by 4,748
- iInfstatement · cited by 1,690
- RingHom.kerstatement and proof · cited by 363
- Ideal.extproof · cited by 131
- RingHom.pistatement · cited by 26
- RingHom.pi_applyproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.ker_Pi_Quotient_mkproof · cited by 1
- Ideal.ker_piRingHom_atPrime_eq_of_pureproof · cited by 1