Theorems · Theorem · commutative algebra

isNoetherian_of_surjective

∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} {P : Type u_4} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid P] [inst_4 : Module R M] [inst_5 : Module S P] {σ : R →+* S}
  [inst_6 : RingHomSurjective σ] (f : M →ₛₗ[σ] P), f.range = ⊤ → ∀ [IsNoetherian R M], IsNoetherian S P

Defined in

Mathlib.RingTheory.Noetherian.Basic

Cited by

4 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleRingHomSurjectiveIsNoetherian