Theorems · Definition · commutative algebra

Localization.AtPrime.mapPiEvalRingHom

{ι : Type u_4} →
  {R : ι → Type u_5} →
    [inst : (i : ι) → CommSemiring (R i)] →
      {i : ι} →
        (I : Ideal (R i)) →
          [inst_1 : I.IsPrime] → Localization.AtPrime (Ideal.comap (Pi.evalRingHom R i) I) →+* Localization.AtPrime I

Localization.localRingHom specialized to a projection homomorphism from a product ring.

Defined in: Mathlib.RingTheory.Localization.AtPrime.Basic
Cited by: 4 results in Mathlib
Foundations: Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring Ideal.IsPrime

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommSemiringstatement and proof · cited by 10,911
RingHomstatement · cited by 10,189
Idealstatement and proof · cited by 4,748
Ideal.IsPrimestatement and proof · cited by 827
Ideal.primeComplstatement · cited by 462
Ideal.comapstatement and proof · cited by 443
Localization.AtPrimestatement · cited by 299
Localization.localRingHomproof · cited by 54
Pi.evalRingHomstatement and proof · cited by 44

Cited by4

Results whose statement or proof uses this declaration.

MaximalSpectrum.toPiLocalization_not_surjective_of_infiniteproof · cited by 2
Localization.AtPrime.mapPiEvalRingHom_algebraMap_applystatement · cited by 0
Localization.AtPrime.mapPiEvalRingHom_bijectivestatement · cited by 0
Localization.AtPrime.mapPiEvalRingHom_comp_algebraMapstatement · cited by 0