Theorems · Theorem · commutative algebra
Ideal.Filtration.Stable.exists_pow_smul_eq
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {I : Ideal R}
{F : I.Filtration M}, F.Stable → ∃ n₀, ∀ (k : ℕ), F.N (n₀ + k) = I ^ k • F.N n₀- Defined in
- Mathlib.RingTheory.Filtration
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement and proof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- add_zeroproof · cited by 2,707
- add_commproof · cited by 1,535
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- add_assocproof · cited by 746
- pow_addproof · cited by 315
- SemigroupAction.mul_smulproof · cited by 291
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.Filtration.Stable.exists_pow_smul_eq_of_geproof · cited by 2