Theorems · Theorem · commutative algebra
LinearMap.eventually_iSup_ker_pow_eq
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [IsNoetherian R M]
(f : M →ₗ[R] M), ∀ᶠ (n : ℕ) in Filter.atTop, ⨆ m, (f ^ m).ker = (f ^ n).ker- Defined in
- Mathlib.RingTheory.Noetherian.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- LE.le.transproof · cited by 3,151
- Filter.Eventuallystatement · cited by 3,134
- iSupstatement · cited by 2,415
- Filter.atTopstatement · cited by 2,405
- LT.lt.leproof · cited by 2,189
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.charpoly_nilpotent_tfaeproof · cited by 2
- LinearMap.isCompl_iSup_ker_pow_iInf_range_powproof · cited by 2