Theorems · Theorem · commutative algebra

LinearMap.eventually_codisjoint_ker_pow_range_pow

∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsArtinian R M]
  (f : Module.End R M), ∀ᶠ (n : ℕ) in Filter.atTop, Codisjoint (f ^ n).ker (f ^ n).range

For any endomorphism of an Artinian module, any sufficiently high iterate has codisjoint kernel and range.

Defined in

Mathlib.RingTheory.Artinian.Module

Cited by

2 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleIsArtinian