Theorems · Theorem · commutative algebra
FiniteMultiplicity.multiplicity_eq_iff
∀ {α : Type u_1} [inst : Monoid α] {a b : α},
FiniteMultiplicity a b → ∀ {n : ℕ}, multiplicity a b = n ↔ a ^ n ∣ b ∧ ¬a ^ (n + 1) ∣ b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- multiplicitystatement and proof · cited by 117
- FiniteMultiplicitystatement and proof · cited by 73
- FiniteMultiplicity.emultiplicity_eq_multiplicityproof · cited by 31
Cited by4
Results whose statement or proof uses this declaration.
- multiplicity_mulproof · cited by 5
- FiniteMultiplicity.exists_eq_pow_mul_and_not_dvdproof · cited by 3
- multiplicity_selfproof · cited by 2
- FiniteMultiplicity.one_rightproof · cited by 0