Theorems · Theorem · commutative algebra

IsNoetherian.noetherian

∀ {R : Type u_1} {M : Type u_2} {inst : Semiring R} {inst_1 : AddCommMonoid M} {inst_2 : Module R M}
  [self : IsNoetherian R M] (s : Submodule R M), s.FG

IsNoetherian R M is the proposition that M is a Noetherian R-module, implemented as the predicate that all R-submodules of M are finitely generated.

Defined in

Mathlib.RingTheory.Noetherian.Defs

Cited by

32 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

IsNoetherian