Theorems · Theorem · commutative algebra

Ideal.map_eq_top_or_isMaximal_of_surjective

∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] (f : F)
  [RingHomClass F R S],
  Function.Surjective ⇑f → ∀ {I : Ideal R}, I.IsMaximal → Ideal.map f I = ⊤ ∨ (Ideal.map f I).IsMaximal

Defined in

Mathlib.RingTheory.Ideal.Maps

Cited by

6 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringFunLikeRingHomClass