Theorems · Theorem · algebraic geometry

RingHom.surjectiveOnStalks_iff_forall_ideal

∀ {R : Type u_1} [inst : CommRing R] {S : Type u_2} [inst_1 : CommRing S] {f : R →+* S},
  f.SurjectiveOnStalks ↔ ∀ (I : Ideal S), I ≠ ⊤ → ∀ (s : S), ∃ x r, ∃ c ∉ I, f r ∉ I ∧ c * f r * s = c * f x

Defined in

Mathlib.RingTheory.SurjectiveOnStalks

Cited by

2 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRing