Theorems · Theorem · ring theory
Module.End.pow_map_zero_of_le
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{f : Module.End R M} {m : M} {k l : ℕ}, k ≤ l → (f ^ k) m = 0 → (f ^ l) m = 0- Defined in
- Mathlib.Algebra.Module.LinearMap.End
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- map_zeroproof · cited by 1,614
- Module.Endstatement and proof · cited by 774
- pow_addproof · cited by 315
- Module.End.mul_applyproof · cited by 23
Cited by6
Results whose statement or proof uses this declaration.
- Module.End.isNilpotent_iff_of_finiteproof · cited by 1
- LieModule.weight_vector_multiplicationproof · cited by 1
- Module.End.eventually_disjoint_ker_pow_range_powproof · cited by 1
- LieSubalgebra.isNilpotent_of_forall_le_engelproof · cited by 1
- LieModule.isNilpotent_toEnd_of_mem_rootSpaceproof · cited by 1
- Module.End.genEigenspace_inf_le_addproof · cited by 1