Theorems · Theorem · commutative algebra
emultiplicity_pow_self
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] {p : α},
p ≠ 0 → ¬IsUnit p → ∀ (n : ℕ), emultiplicity p (p ^ n) = ↑n- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- IsUnitstatement and proof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- IsCancelMulZerostatement and proof · cited by 177
- emultiplicitystatement · cited by 156
- dvd_reflproof · cited by 97
- emultiplicity_eq_of_dvd_of_not_dvdproof · cited by 5
- pow_dvd_pow_iffproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- multiplicity_pow_selfproof · cited by 2
- Nat.Prime.emultiplicity_pow_selfproof · cited by 1
- emultiplicity_pow_self_of_primeproof · cited by 1