Theorems · Theorem · commutative algebra

LinearMap.isCompl_iSup_ker_pow_iInf_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]
  [IsNoetherian R M] (f : M →ₗ[R] M), IsCompl (⨆ n, (f ^ n).ker) (⨅ n, (f ^ n).range)

This is the Fitting decomposition of the module M with respect to the endomorphism f. See also LinearMap.eventually_isCompl_ker_pow_range_pow for an alternative spelling.

Defined in

Mathlib.RingTheory.Artinian.Module

Cited by

2 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleIsArtinianIsNoetherian