Theorems · Theorem · commutative algebra

Module.End.isNilpotent_restrict_of_le

∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {f : Module.End R M} {p q : Submodule R M} {hp : Set.MapsTo ⇑f ↑p ↑p} {hq : Set.MapsTo ⇑f ↑q ↑q},
  p ≤ q → IsNilpotent (LinearMap.restrict f hq) → IsNilpotent (LinearMap.restrict f hp)

Defined in: Mathlib.RingTheory.Nilpotent.Lemmas
Cited by: 3 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Quot.sound
Assumes: Semiring AddCommMonoid Module

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Cites17

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · 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
SetLike.coestatement and proof · cited by 8,199
Submodulestatement and proof · cited by 7,192
LinearMap.extproof · cited by 844
Module.Endstatement and proof · cited by 774
Set.MapsTostatement and proof · cited by 732
DFunLike.congr_funproof · cited by 288

Cited by3

Results whose statement or proof uses this declaration.

Module.End.disjoint_genEigenspaceproof · cited by 7
Module.End.isNilpotent_restrict_maxGenEigenspace_sub_algebraMapproof · cited by 1
Module.End.isNilpotent_restrict_genEigenspace_topproof · cited by 0