Theorems · Theorem · commutative algebra

LinearMap.isNoetherian_iff_of_bijective

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {S : Type u_3}
  {P : Type u_4} [inst_3 : Semiring S] [inst_4 : AddCommMonoid P] [inst_5 : Module S P] {σ : R →+* S}
  [RingHomSurjective σ] (l : M →ₛₗ[σ] P), Function.Bijective ⇑l → (IsNoetherian R M ↔ IsNoetherian S P)

Defined in

Mathlib.RingTheory.Noetherian.Basic

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleSemiringAddCommMonoidModuleRingHomSurjective