Theorems · Inductive type · commutative algebra
IsNoetherian
(R : Type u_1) → (M : Type u_2) → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [Module R M] → Prop
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
- 208 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement · cited by 20,661
- Semiringstatement · cited by 13,802
- AddCommMonoidstatement · cited by 12,281
Cited by231
Results whose statement or proof uses this declaration.
- IsNoetherianRingproof · cited by 268
- IsNoetherian.noetherianstatement and proof · cited by 32
- LieModule.chainTopCoeffstatement and proof · cited by 30
- LieAlgebra.corootSpacestatement and proof · cited by 23
- LieModule.chainBotCoeffstatement and proof · cited by 22
- LinearMap.HasNoetherianRangeproof · cited by 21
- LieModule.chainTopstatement and proof · cited by 20
- isFiniteLength_iff_isNoetherian_isArtinianstatement and proof · cited by 14
- Module.Finite.of_injectivestatement and proof · cited by 10
- LieAlgebra.rootSpace_zero_eqstatement and proof · cited by 9
- LieModule.coe_chainTopstatement and proof · cited by 9
- monotone_stabilizes_iff_noetherianstatement · cited by 8
Showing the 200 most cited of 231.