Theorems · Theorem · commutative algebra
multiplicity_pow_self
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] {p : α},
p ≠ 0 → ¬IsUnit p → ∀ (n : ℕ), multiplicity p (p ^ n) = n- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 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.
- IsUnitstatement and proof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- IsCancelMulZerostatement and proof · cited by 177
- multiplicitystatement · cited by 117
- multiplicity_eq_of_emultiplicity_eq_someproof · cited by 11
- emultiplicity_pow_selfproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_oneproof · cited by 4
- multiplicity_pow_self_of_primeproof · cited by 1