Theorems · Definition · commutative algebra
IsNilpotent.exp
{A : Type u_1} → [inst : Ring A] → [Module ℚ A] → A → AThe exponential map on algebras, defined in analogy with the usual exponential series. It provides meaningful (non-junk) values for nilpotent elements.
- Defined in
- Mathlib.RingTheory.Nilpotent.Exp
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Ringstatement and proof · cited by 7,463
- Finset.sumproof · cited by 5,195
- Finset.rangeproof · cited by 1,341
- Nat.factorialproof · cited by 616
- nilpotencyClassproof · cited by 12
Cited by15
Results whose statement or proof uses this declaration.
- IsNilpotent.exp_eq_sumstatement · cited by 5
- IsNilpotent.exp_add_of_commutestatement and proof · cited by 3
- IsNilpotent.map_expstatement · cited by 2
- LieDerivation.expproof · cited by 2
- IsNilpotent.exp_zerostatement · cited by 2
- LieDerivation.exp_applystatement · cited by 1
- Module.End.commute_exp_left_of_commutestatement and proof · cited by 1
- IsNilpotent.exp_mul_exp_neg_selfstatement and proof · cited by 1
- IsNilpotent.exp_neg_mul_exp_selfstatement and proof · cited by 1
- IsNilpotent.isUnit_expstatement and proof · cited by 0
- LieDerivation.exp_map_applystatement · cited by 0
- IsNilpotent.exp_smul_eq_sumstatement · cited by 0