Theorems · Theorem · commutative algebra

Module.End.eventually_disjoint_ker_pow_range_pow

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [IsNoetherian R M]
  (f : Module.End R M), ∀ᶠ (n : ℕ) in Filter.atTop, Disjoint (f ^ n).ker (f ^ n).range

For an endomorphism of a Noetherian module, any sufficiently large iterate has disjoint kernel and range.

Defined in

Mathlib.RingTheory.Noetherian.Defs

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleIsNoetherian