Theorems · Theorem · commutative algebra
IsNilpotent.exp_smul_eq_sum
∀ {A : Type u_1} [inst : Ring A] [inst_1 : Module ℚ A] {M : Type u_2} [inst_2 : AddCommGroup M] [inst_3 : Module A M]
[inst_4 : Module ℚ M] {a : A} {m : M} {k : ℕ},
a ^ k • m = 0 → IsNilpotent a → IsNilpotent.exp a • m = ∑ i ∈ Finset.range k, (↑i.factorial)⁻¹ • a ^ i • m- Defined in
- Mathlib.RingTheory.Nilpotent.Exp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Finset.sumstatement and proof · cited by 5,195
- add_zeroproof · cited by 2,707
- Finset.sum_congrproof · cited by 2,323
- Finset.rangestatement and proof · cited by 1,341
- smul_zeroproof · cited by 665
- Nat.factorialstatement and proof · cited by 616
- Finset.Icoproof · cited by 450
- SemigroupAction.mul_smulproof · cited by 291
- le_or_gtproof · cited by 269
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.