Theorems · Theorem · algebraic geometry

PrimeSpectrum.denseRange_comap_iff_minimalPrimes

∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f : R →+* S),
  DenseRange (PrimeSpectrum.comap f) ↔
    ∀ (I : Ideal R) (h : I ∈ minimalPrimes R), { asIdeal := I, isPrime := ⋯ } ∈ Set.range (PrimeSpectrum.comap f)

[Stacks Tag 00FL](https://stacks.math.columbia.edu/tag/00FL)

Defined in

Mathlib.RingTheory.Spectrum.Prime.Topology

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiring