Theorems · Theorem · commutative algebra
isNoetherian_iff_fg_wellFounded
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
IsNoetherian R M ↔ WellFoundedGT { N // N.FG }- Defined in
- Mathlib.RingTheory.Noetherian.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.ofPredproof · cited by 6,101
- Bot.botproof · cited by 4,720
- Submodule.spanproof · cited by 1,504
- OrderEmbeddingproof · cited by 619
- LE.le.antisymmproof · cited by 507
- bot_leproof · cited by 306
Cited by1
Results whose statement or proof uses this declaration.
- IsBezout.TFAEproof · cited by 2